Phys  311/312

last updated March 6, 2008

Introduction to Modern Physics

these two courses are considered to be a sequence, so it does not make sense to join phys 312 without proper preparation by either phys 311 or some similar course taken somewhere else 

Instructor: Peter Moeck (Ph.D., Dr. rer. nat.), Assistant Professor of Physics

Office:  Cramer Hall, room 183

Office hours: Tuesday and Thursday: 12.00 – 12:30 pm (you can walk with me up to the office, right after class)

e-mail: pmoeck@pdx.edu   web: http://www.physics.pdx.edu/~pmoeck/index.html

telephone: 503 725 4227 (but I do prefer communicating per e-mail with my students and I don’t read attachments to e-mails as a matter of principle, (don’t send e-mail attachments to me, e.g. late homeworks, I do not open them as a matter of principle. late homeworks can however be send as attachments to our teaching assistant/ grader Mr. Daeyoung Woo:  daeyoung@pdx.edu the homeworks will get posted each week on Thursday afternoon, http://web.pdx.edu/~daeyoung/

Daeyoung’s office hours are Tuesday 1:30 to 2 pm, and Wednesday 10:00 to 11:00 am, his telephone umber is 5 2695, it office is opposite to the lab of Prof. John Freeouf, Science Building 1 in the basement, it’s best to call first

This is a two quarter course, everybody that enrolls only in the second term is assumed to have sufficient knowledge in Modern Physics form some other course !

It is best to take the two courses within one academic year as there will be frequent references back to the material covered in the first quarter throughout the second quarter !!

Lectures Phys 312: Tuesdays and Thursdays 10:00 – 11:50 am (five minutes break at about 10:55) at Cramer Hall, room 183

you better come to the lectures as it is the things I pay special emphasis to in the lectures that will be asked off you in the tests and exams, but I do not take a register

Homework credit contribute 30 % to your final course grade (you better do your homework as this will prepare you well for the tests and final exam, if you don’t at all you will get zero credit in this section!), Homeworks will be set on this webpage on Thursday late afternoon/evening. Homeworks have to be handed in on Tuesdays before the lecture, as their solutions will be posted soon after this but on the web (but no later than Wednesday late afternoon/evening). Credit is given for solution of even and odd problems, but don’t just copy the correct answer of an odd problem from the back of the textbook - that will give you no credit at all (even if the final result is correctly copied). The majority of problems will be of the “even type”. All homework solutions will be published on this webpage.

your final grade will be calculated from your individual scores:

                        30 % Home works

                        30 % Midterm exam

                        40 % Final exam, all topics after 10 weeks,

the exam questions will frequently be similar to homework questions but it will be biased towards the tougher ones, so you better check very carefully what went wrong in the homeworks so that you do best in the exams, solutions of homeworks and midterm exam will be posted at http://www.physics.pdx.edu/~pmoeck/modern_physics.htm, solutions of final exams can be obtained personally at office hours.

These final grade percentages make sure you have 60 % of your grade made up before the final exam, so there is no need to get nervous at exam time as the final is unlikely to change much.

You get to keep your graded midterm exam, the final exams remain with me and you can look at them at office hours.

Final exam date: as set by PSU

highly recommended text: Concepts of Modern Physics by A. Beiser, McGraw-Hill, 6th edition, 2002, 542 pages, (quite easy going but pretty much to the point, a few bits and pieces missing, but a good thread throughout) you may get the paperback version over www.tatamcgrawhill.com or over www.amazon.com

other main texts:

Modern Physics by R.A. Serway, C.J. Moses, and Moyer 3rd edition, Saunders 2005, 600 pages without appendices and index, it’s pretty good, I served as one of the accuracy reviewers – if you are just coming for 311, that should be your book, if you do the whole sequence 311 and 312 I recommend Beiser

Modern Physics for Scientists and Engineers by Stephen T. Thornton and Andrew Rex, 3rd edition, Brooks/Cole, 2006, about 600 pages without appendices, (good and comprehensive most of the time, sometimes too much detail and not enough explanations of the more important concept)

Modern Physics for Scientist and Engineers by John R. Taylor, Chris D. Zafiratos, Michael A. Dubson, 2nd edition, Prentice Hall, 2004, 720 pages, (many good examples in the text, good reviews of classical physics concepts from time to time, comprehensive atomic mass table, operators and expectation values first show up in the section on the hydrogen atoms, rather than in the section on quantum mechanics in one dimension, makes it a bit more difficult than perhaps necessary,)

Modern Physics by P.A. Tipler, R.A. Llewellen, 5th edition, Freeman, 2007 (a bit heavier but the classical text for the serious student, best on “postmodern” particle physics and cosmology, I served as one of the chapter/concept reviewers)

Modern Physics by J. Bernstein, P.M. Fishbane and S. Gasiorowicz, Prentice Hall, 2000. 602 pages, (pretty tough going at places as it is written by theorists; as it is a new text, sometimes comprehensive explanations are not provided in sufficient detail) 

Modern Physics by R.A. Serway and C.J. Moses, 1st edition, about 500 pages without index, by the way, don’t purchase the 2nd edition (Saunders, 1997) including MP Desktop software that is supposed to help the students and lots of optional text which kind of makes it difficult to follow the thread) – my 2002/2003 students didn’t like it much,

Modern Physics by Kenneth Krane, 2nd edition, Wiley, 1995, 581 pages, (least mathematical, more conceptual, frequent connections to classical physics, quite easy going, sometimes too simplistic for my liking, but a good book)

Modern Physics by Hans C. Ohanian, 2nd edition, Prentice Hall, 457 pages without appendices, (a bit week on solid state physics but otherwise OK, mathematical level is moderate)

Modern Physics from α to Z0 by James W. Rohlf, John Wiley and Sons. Inc., 1994, 569 pages plus some 60 pages appendix, good book for very dedicated students, but somewhat unconventional sequence in presenting the material, i.e. it starts with a survey of particles and forces and within some 20 pages arrives at Feynman diagrams and the fine structure constant, which other text may cover at page 200 or so in case of the fine structure constant (or not at all in case of Feynman diagrams). The Lorentz transformations, on the other hand, only come up after some 100 pages. Since the book is published 1995, the top quark is missing, …, but  the physics is sound. It is almost like a reference book rather than a undergraduate textbook. Perhaps there were no further editions because not many instructors adopted this text for their classes for students with mixed background?

a complementary book for worked problems: Schaum’s Outlines Modern Physics, by R. Gautreau and W. Savin, 2nd edition, Mc Graw-Hill, 1999

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a nice book that “builds a bridge between introduction to modern physics and real quantum mechanics is A. I. M. Rae, Quantum Mechanics, CRC Press, Boca Raton, Ann Arbor, London, Tokyo, 5th edition, 2007

free *.pdf files on:     general introduction to quantum mechanics,

                                    one-dimensional Schrödinger equation,

                                    three-dimensional Schrödinger equation, and 

                                    further details on the book where these chapters are from

                                    (it’s European university course stile, not expensive, no

                                    examples within the text, but pretty much to the point, if you like doing maths,

                                    this book very well complements the course)

       

this book introduces just 4 postulates from which all of quantum mechanics can be developed

 

 

The basic postulates of quantum mechanics

 

“1. For every dynamical system there exist a wavefunction that is a continuous, square-integrable, single-valued function of the parameters of the system and of time, and from which all possible predictions about the physical properties of the system can be obtained.

 

2. Every dynamical variable may be represented by a hermitian operator whose eigenvalues represent the possible results of carrying out a measurement of the value of the dynamical variable. Immediately after such a measurement, the wavefunction of the system is identical to the eigenfunction corresponding to the eigenvalue obtained as a result of the measurement.

 

3. The operators representing the position and momentum of a particle are vector r and –i h-barÑ respectively. Operators representing other dynamical quantities bear the same functional relations to these, as do the corresponding classical quantities to the classical position and momentum variables.

 

4a. When a measurement of a dynamical variable represented by the hermitian operator Q is carried out on a system whose wavefunction is y, then the probability of the result being equal to a particular eigenvalue qn will be ½an2 ½, where y = å an fn are the eigenfunctions corresponding to the eigenvalues qn.”

 

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4b. In other words: When a measurement is made, the result is one of the eigenvalues of the operator associated with the measurement. As a result of the measurement, the wavefunction collapses into the corresponding eigenfunction. The probability of a particular outcome equals the squared modulus of the overlap between the wavefunction before and after the measurement.

 

From this follows mathematically that  Dx Dp ≥ ½ ½<[x, –i h-bar Ñ]>½= ½ h-bar (i.e. Heisenberg’s uncertainty principle)

 

which corresponds physically to the fact that it is impossible to decide in a double slit experiment with a single particle through which hole the particle went without destroying the interference pattern of the corresponding quantum mechanical object (Feynman’s uncertainty principle”!

 

Between measurements, the development of the wavefunction with time is governed by time-dependent Schrödinger Equation and completely deterministic. Measurement generally leads to a “collapse” of the wavefunction into one of the eigenfunctions of the measurement operator. This collapse is not “caused by” or “associated with” by the Schrödinger Equation itself, but constitutes a “separate type” of time dependency that is associated with the act of measurement. So there are two different types of time dependency within the framework of quantum mechanics in the Copenhagen interpretation and this fact is know as the “quantum measurement problem”.

 

One of the strength of A. I. M. Rae’s text is that a whole chapter is dedicated to explain this problem in more detail.  

 

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I use all of these text books to prepare my lectures, probably I use Beiser, Serway et al., Thornton & Rex, Taylor et al., Krane, the most (possibly in this order). You may work with anyone of them or with previous editions of these books, the homework problems will be given on the webpage and may be from either the Beiser or the Serway text texts. So I am not forcing you of purchasing any one text, it’s up to you, you are responsible adults. If you are short of money, I can lend you a few current and older versions of these texts as long as supplies last, supplies are depleted a bit since some students never returned they lend from me.

further reading and real fun to read at bedtime and very useful to explain modern physics to your

grandparents and kids:

 

Sheldon L. Glashow, From Alchemy to Quarks, Brooks/Cole, 1994, this is the text the Nobel prize winning author uses to teach physics to non-science majors, so it is essentially non-mathematical, but concepts are very clearly expressed verbally My course gained a lot from this book as Glashow writes: “There is but one culture of which science is an essential part. Membership in the community of educated men and women demands competence in science and awareness of its history.”

 

Physics for Scientists and Engineers with Modern Physics, Serway/Jewett, 6th edition, Volume 5, ISBN 0-534-40854-0, )there is now a 7th edition.)

paperback (it is volume 5 of the 5 volume set which has a different ISBN, covering  only chapters 39-46 so don’t purchase the

whole set if you already have a good undergraduate text on classical physics, Thomson Brooks/Cole (everything is a bit

simpler, just enough material for a one quarter course, if I have to give Phys 313 “Ideas in Modern Physics”, 

http://www.physics.pdx.edu/course_info.htm#300  - that will be the text I am going to use, I served as a chapter reviewer for this text)

 

Introduction to Quantum mechanics in Chemistry, Materials Science, and Biology, by S. M. Blinder, Elsevier 2004, only about $40 but pretty good if you are aiming in a career in these professions, not so much use for a prospective physicist

 

Wolfgang Rindler, Relativity, Special, General and Cosmological, 2nd edition, Oxford University Press, 2006

 

Physics for Poets, 5th edition, McGraw Hill, 2003, by Robert H. March (which is at the mathematical level that was taught at Moslem

universities from Toledo to Timbuktu before the fourteenth century, i.e. Algebra no calculus)

 

In Search of Schrödinger’s Cat, Quantum Physics and Reality, John Gribbin, paperback, parallel worlds and all the rest of it, pretty nice if you don’t like the COPENHAGEN interpretation of quantum mechanics for aesthetical or philosophical reasons

 

and Physics and Philosophy, the revolution in modern science by W. Heisenberg, Harper Torchbooks, 1962, a bit heavier although without any mathematics as he gets philosophical

 

go also to http://www.whfreeman.com/modphysics/INDEX.HTM#top for lots of interesting modern physics stuff  by Tippler et al., to be downloaded as *.pdf

 

an interesting paper, partly philosophical/partly “quantum physically”, from a Visiting Professor at Portland State and author of widely read books on quantum mechanics: A new interpretation on Quantum Mechanics. I am in no position to judge if all the claims in this paper are correct, but have a go yourself, your opinion is as valuable as mine.

 

Some students - frequently those with strong religious beliefs - don’t like the probabilistic interpretation of quantum mechanics according to the so called Copenhagen School (Bohr, Born, Heisenberg). Well there may or may not be an alternative in the form of Bohm’s version of quantum mechanics, and here is a link to an article published in Scientific America that may serve as a starting point in exploring Bohm’s version of quantum mechanics. Sure this article is a bit polemic as its author wants to push his book, but it concedes that all predictions of quantum mechanics are borne out in experiments. Interestingly, Bohm’s version makes exactly the same prediction and can thus also claim to be in agreement with all of the experimental evidence - sure the price is also an uncertainty principle. Only in Bohm’s version the uncertainty principle takes a different form, so in effect Bohm’s version of quantum mechanics proofs nothing beyond the point that one actually does not need to stick to the Copenhagen Interpretation in order to make progress in quantum mechanics.  (Bohm’s theory builds on de Broglie’s work and is a so called hidden variable theory. A new idea is the “quantum potential” that in a sense makes the difference between quantum mechanics and classical mechanics, but is a concept closer to Aristotle than to Newton, … so there are some loose ends as well.)

 

 

Our homework grader is graduate’PhD student: Mr. Daeyoung Woo:  daeyoung@pdx.edu, of the Physics Department, Science Building  office hours Wednesday  10:00 to 11:00 am and Tuesday 1:30 – 2.00 pm and by special appointment, email him first, he will tell you where you can meet.  

 

Your homework questions will be selected from the Beiser text, the Serway text, and possibly the Thornton and Rex text. The respective homework section pages will be accessible over this webpage, doing that, grading your homeworks and midterm exams is Daeyoung’s job)

 

For discussion on the homework problems and their grading you have to approach Mr. Woo  first, only if you can’t resolve the matter with her will I talk to you about them. Similarly, only if Daeyoung agrees will your homework score be changed, do not postpone issues with her up to the last week!

 

What will be covered in Phys 311/312?

 

The revolutions in the concepts of physics in the early 20th century: special relativity, Introduction to quantum mechanics:  black-body radiation, energy quantum ideas, Bohr/Rutherford theory of the atom, Schrödinger equation, wave functions, electronic structure of atoms, periodic table, nuclear structure, radioactivity, fission and fusion, (+ very briefly: statistical physics and solid state physics). Prerequisite:  Ph 203, or Ph 213 and Mth 252, PH 312 is to be taken after PH 311 or a similar one quarter/one semester course elsewhere, it does make no sense at all to show up for phys 312 without proper introduction to the subject

 

“There is something fascinating about science. One gets such wholesale returns of conjecture out of such trifling investment of facts.” Mark Twain, Life on the Mississippi

 

  hear him speak, he does have a really nice German accent:

 

"Ladies and gentlemen, our age is proud of the progress it has made in man's intellectual development. The search and striving for truth and knowledge is one of the highest of man's qualities - though often, the pride is most loudly voiced by those who strive the least. And certainly we should take care not to make the intellect our god; it has, of course, powerful muscles, but no personality. It cannot lead, it can only serve; and it is not fastidious in its choice of a leader. This characteristic is reflected in the qualities of its priests, the intellectuals…"

 

“But in physics, I soon learned to scent out the path that led to the depths, and to disregard everything else, all the many thing that clutter up the mind, and divert it from the essential. The hitch in all this was, of course, the fact that one had to cram all this stuff into one’s mind for the examination, whether one liked it or not.”

 

“In living through this so-called great epoch, I find it difficult to believe that I belong to such an idiotic, rotten species. The species that actually boasts of his freedom of will, heroism on command, senseless violence, and all the loathsome nonsense that goes by the name of patri…..”

 

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have a look here at THE PAPER with which it all started, a complete version of this paper is also available for the serious student

 

towards the end of the course you have to read and we will discuss a Review PAPER on just a few examples how quantum mechanics are going to be used in the near future

 

a statement from a more recent American master of this field

 

Richard P. Feynman in chapter 1 of “QED, the strange theory of light and matter”

 

“… I’d like to talk a little bit about understanding. When we have a lecture, there are many reasons why you might not understand the speaker. One is, his language is bad – he doesn’t say what he means to say, or he says it upside down – and it’s hard to understand. That’s a rather trivial matter, and I’ll try my best to avoid to much of my New York (German – my insertion) accent.

 

Another possibility, especially if the lecturer is a physicist, is that he uses ordinary words in a funny way. Physicist often use ordinary words as “work” or “action” or “energy” or even, as you shall see, “light” for some technical purpose. Thus, when I talk about “work” in physics, I don’t mean the same thing as when I talk about “work” on the street. During this lecture I might use one of those words without noticing that it is being used in this unusual way. I’ll try my best to catch myself – that’s my job – but it is an error that is easy to make.

 

The next reason that you might think you do not understand what I am telling you is, while I am describing to you how Nature works, you won’t understand why Nature works that way. But you see, nobody understands that. I can’t explain why Nature behaves in this peculiar way.

 

Finally, there is this possibility: after I tell you something, you just can’t believe it. You can’t accept it. You don’t like it. A little screen comes down and you don’t listen anymore, I’m going to describe to you how Nature is – and if you don’t like it, that’s going to get in the way of your understanding it. It’s a problem that physicists have learned to deal with: They’ve learned to realize that whether they like a theory of they don’t like a theory is not the essential question. Rather, it is whether or not the theory gives predictions that agree with experiment. It is not a question of whether a theory is philosophical delightful, or easy to understand, or perfectly reasonable form the point of view of common sense. The theory of quantum electrodynamics describes nature as absurd form the point of view of common sense. And it agrees fully with experiment. …”

 

Phys 311

 

Homework Problems ( Beiser, Serway at al., Thornton/Rex in different directories): the respective homework pages are accessible here, you just pick the right problem number from the right chapter and solve them, hand them in each week Tuesday before class, if you can’t make it to class that day send them with the same deadline as email attachment to Daeyoung Woo  daeyoung@pdx.edu  (not to me I don’t open attachments anyhow) with a brief excuse, if you are past the deadline you really need a good excuse that can be backed up one way or another, if your excuse is too “strange”, I’ll ask the class what they think – if your homework should still be graded or not. DEAL? Each week 3 problems, each of them carries 5 points!

5 problems for the first and second week combined set at Thursday of the second week due on the Tuesday of the third week..

 

18 lectures

1 mid term test,

homeworks,

1 final exam

Questions to be address

Material covered

Homework, (due Tuesdays before lecture starts unless otherwise stated), other comments, links to solutions of homework problems and tests, other comments

25,27 September

 

show up with an open mind

 There is absolutely no replacement for your reading of the text !!!

 

What is modern physics?

Why is it important?

Relative to what is the speed of light measured?

Galilean relativity, Michelson-Morley experiment, Lorentz transformations, length contraction, time dilation

lecture manuscript for relativity can be downloaded/printed as *.doc  or *.pdf

 

for an alternative approach to relativistic mechanics that does not use the concept of relativistic mass, about which Einstein said ”not good … no clear definition can be given. It is better to introduce no other mass concept that the rest mass” click here, relativistic momentum is explained by the concept of relativistic velocity – the so called “One map two clock approach”  

 

Homework Problems ( Beiser, Serway at al., Thornton/Rex in different directories):

This week all from Beiser, Problem 4, 8, 18, 20, 24, good luck

 

4. An observer on a spacecraft moving at 0.700 c relative to the earth finds that a car takes 40.0 min to make a trip. How long does the trip take to the driver of the car?

 

8. The Apollo 11 spacecraft that landed on the moon in 1969 traveled there at a speed relative to the earth of 1.08 104 m/s. To an observer on the earth, how much longer than his own day was a day on the spacecraft?

 

18. An astronaut is standing in a spacecraft parallel to its direction of motion An observer on the earth finds that the spacecraft speed is 0.60c and the astronaut is 1.3 m tall. What is the astronaut’s height as measured in the spacecraft?

 

20. A meter stick moving with respect to an observer appears only 500 mm long to her. What is its relative speed? How long does it take to pass her? The meter stick is parallel to its direction of motion.

 

24. (a) An electron’s speed is doubled from 0.2c to 0.4c. By what ratio does its momentum increase? (h) What happens to the momentum ratio when the electron’s speed is doubled again from 0.4c to 0.8c?

 

October 2/4

What are the nuts and bolts of relativity?

 

 

Einstein’s PhD thesis submission

at University of Bern,

 

Relativistic kinematics and dynamics, Summary relativity

 

Non-mathematic General relativity

 

Blackbody Radiation Photoelectric effect X-rays (briefly)

 

 

 

October 9/11

 

Compton effect

Particle-Wave complementarity

From now on just 3 problems per week, all 5 points in total, this time from Serway et al.

 

Chapter 2. Find the speed of a particle whose total energy is 50% greater than its rest energy.

 

chapter 3,

problem 2. The temperature of your skin is approximately 35ºC/ What is the wavelength at which the peak occurs in the radiation emitted from your skin?

 

Problem 4. (a) Use Stefan’s law to calculate the total power radiated per unit area by a tungsten filament at a temperature of 3000K. (Assume that the filament is a an ideal radiator). (b) If the tungsten filament of a lightbulb is rated at 75 Watt, what is the surface area of the filament? (Assume that the main energy loss is due to radiation.)

 

Can something be a particle and a wave at the same time?

 

 

lecture manuscript for chapter 2 (quantum theory of light) can be downloaded I word format here and here in pdf

 

October 16/18

 

I have to give a lecture in Seattle at an international conference at the very same time our class meets, my postdoctoral researcher, Dr. Peter Sondergeld will cover this class

Who was Konrad Wilhelm Röntgen? A physician? What is his legacy? What did Max von Laue get his Noble prize for?

 

 

 

J.J. Thomson’s discovery of the electron

Read the Planck PAPER and answer he following questions: Which novel idea(s) did Planck introduce in the derivation of his black body radiation  formula? In which § do(es) it (they) first show up?  What are (is) the equation number(s) relating to this ( these) new idea(s)? Where did he get an estimate of h from? 

Read there is also an complete version of the Planck PAPER translated by somebody else

 

 

 

October 25

Is matter kind of like a plum pudding – the plums having cores?

Rutherford’s discovery of the nucleus

Applied Modern Physics

X-ray, electron and neutron  diffraction, crystallography,

materials science

lecture manuscript for chapters 4/3 can be downloaded here

 

lecture manuscript for Applied Modern Physics can be downloaded as *.doc or *.pdf

 

30 October

 

to ensure that everybody has the same materials, you can bring your own individual printouts of the formulae sheets for chapter 1 can be downloaded/printed as *.pdf no.1 and no.2

L. de Broglie’s PhD thesis Electron wave groups (packets)

electron diffraction mathematics of waves, wave particle duality

 

Homework due on this very day:

 

 

Thornton-Rex, 2nd edition: chapter 3: What is the threshold frequency of the photoelectric effect on lithium (work function 2.9 eV)? What is the stopping potential if the wavelength of the incident light is 400 nm?

 

Thornton-Rex, 2nd edition: chapter 4

 

14. The radius of a hydrogen nucleus is believed to be 1.2 10-15 m. (a) If an electron moves around the nucleus at that very radius, what would be its speed according to the planetary model? (b) What would the total energy be? (c) Are these values reasonable?

 

22. What is the speed (ratio of v/c) of the electron in the first three Bohr orbits of the H atom?

 

lecture manuscript for chapters 4/3 can be downloaded here

 

 

November 6

 

Midterm exam week

Tuesday 10:00 to 11:00.

 

Material from all the chapters we have been discussing so far, independent on how they might be presented in your book, i.e. relativity, quantum theory of light (particle properties of waves), atomic structure (particle nature of matter)

 

 

 

 

 

 

 

 

 

Heisenberg’s uncertainty principle Wave-Particle duality

Beiser chapter 4:

 

No. 20: Find the wavelength of the spectral line that corresponds to a transition in hydrogen from the n = 6 stat to the n = 3 state. In what part of the spectrum id this wavelength?

 

No. 22: How much energy is required to remove an electron in the n=2 state from a hydrogen atom?

 

No. 28: Of the following quantities, which increase and which decrease in the Bohr model as n increases? Frequency of revolution, electron speed, electron wavelength, angular momentum, potential energy, kinetic energy, total energy.

 

 

 

 

 

Serway chapter 5:

Calculate the de Broglie wavelength for an electron with kinetic energy (a) 50 eV and (b) 50keV

 

A ball of mass 50 g moves with a speed of 30 m/s. If its speed is measured to an accuracy of 0.1%, what is the minimum uncertainty in its position?

 

Show that the de Broglie wavelength of an electron accelerated from rest through a small potential difference V is given by λ=1.226 dived by square root of V, where λ is in nanometers and V is in volts

 

 November 9

 

 

lecture manuscript for chapter 5 can be downloaded here

Problems chapter

 

November 15

 

 

Homeworks, Thornton/Rex, Chapter 5

 

22. A (harmonic) wave of wavelength 4 cm has a wavespeed of 4 cm/s. What is its (a) frequency, (b) period, (c) wave number, and (d) angular frequency?

 

40. Find the minimum uncertainty in the speed of a bacterium having mass 3 x 10-15 kg if we know the position of the bacterium to within 1 micrometer, that is, to about its own size.

 

48. Most of the particles known to physicist are unstable. For example the lifetime of the neutral pion is about 10-16 s. Its mass is 135 MeV/c-squared. What is the energy width of this particle (in its ground state)?

 

 

 

 

November 16

 

Quantum mechanics in one dimension

 

homework answers are here either as *doc or *.pdf

November 20

 

 

Homeworks, as agreed 6 problem now, due next Tuesday

Thornton-Rex: Chapter 1, problem 32: a proton and an antiproton are moving towards each other in a head-on collision. It each has the speed of 0.8 c with respect to the collision point, how fast are they moving with respect to each other?

 

Chapter 1, problem 90: An electron has a total energy that is 200 times its rest energy. Determine its (a) kinetic energy, (b) speed, and (c) momentum.

Thornton-Rex: Chapter 2: problem 40: If a 6 keV photon scatters from a free electron at rest, what is the change in the photon’s wavelength if the photon recoils at 90 degrees?

Thornton-Rex: Chapter 5, Problem 16: What is the de Broglie wavelength of the 1 TeV protons accelerated in the Fermi National Laboratory Tevatron accelerator?

Thornton-Rex: Chapter 6: problem 4: Normalize the wave function for a free particle (that travels to the right) in the region x = 0 and x = a.  

Out of the top of my head: Demonstrate that the wave function of a free particle (that travels to the right) is a solution to Schroedinger’s time dependent wave equation. Hint: proceed analogously to what I have showed in class for a harmonic classical wave and the Helmholtz wave equation.

23 November

 

 

Thanksgiving weekend

 

 

 

 

lecture manuscript for chapter 6 can be downloaded/printed here

 

the manuscript on tunneling/frustrated total internal reflection in electromagnetic and water waves can be downloaded here

 

November 28

 

 

Homework

 

 

 

 

 

 As a special treat, you will hear Feynman giving a lecture out of the computer system in class, lecture manuscript for Feynman’s 1st lecture can be downloaded here in word and here in pdf

lecture manuscript for Feynman’s 2nd lecture can be downloaded here in word and here in pdf

4 December, final

The exam is scheduled by PSU

Good luck and preparation

Bring a pocket calculator and your formulae sheets, good luck

 

 

If it is wheels within wheels, you look for the innermost wheel, but if it isn’t you look for whatever the hell it is you find. Richard P. Feynman
 		 

Watch him give The Douglas Robb Memorial Lectures at 
 
http://www.vega.org.uk/video/subseries/8

 

(streaming video for free)

 

 

 

 

 

Grades will be available over the internet

all the best for your holidays and see you all next year for phys 312 !!!

have some fun at http://physicsweb.org/article/world/16/9/2

 

Phys 312 – last updated March 6, 2008

 

same times and days of the week as Phys 311, but sometimes different location, so check out the PSU schedule

 

Cramer Hall, room 183

My office hours as every other year: Tuesday and Thursday: 12.00 – 12:30 pm,

The grader for this course isMr. Daeyoung Woo: daeyoung@pdx.edu , the homeworks will get posted each week on Thursday afternoon, http://web.pdx.edu/~daeyoung/ Daeyoung’s office hours are Tuesday 1:30 to 2 pm, and Wednesday 10:00 to 11:00 am, his telephone umber is 5 2695, it office is opposite to the lab of Prof. John Freeouf, Science Building 1 in the basement, it’s best to call first

Your recommended preparation for these lectures, always read respective chapters in either of the main texts in advance

 

 

 

 

 

 

 

 

Questions to be address

Material covered

Homework, due Tuesday each week before lecture starts*

January 8

 

 

What is modern physics, what is the essence of a wave function,

Now it is getting pretty mathematical, so you better read ahead all of chapter 5 or 6, Schroedinger equation in one dimension!

 

lecture manuscript for chapter 5 can be downloaded here

 

 

Quantum mechanics in 3D,

Starting off with a particle in a 3D box with infinitely high and thick walls, from that going over to the special form of the hydrogen atom potential

From Serway, chapter 6, problems 8 and 16 as set last year,

 

1. A bead of mass 5.00 g slides freely on a wire 20 cm long. Treating this system as a particle in a one-dimensional box, calculate the value of n corresponding to the state of the bead if it is moving with a speed of 0.1 nm per year (that is, apparently at rest.)

 

2. An electron is trapped in an infinitely deep potential well 0.3 nm in width. (a) If the electron is in the ground state, what is the probability of finding it within 0.1 nm of the left-hand wall? (b) Repeat (a) for an electron in the 99th excited state (n = 100). (c) Are your answers consistent with the correspondence principle?

 

3. Find the points of maximum and minimum probability density for the nth state of a particle in a one-dimensional infinitely deep box. Check your result for the n = 2 state.

 

4. The wavefunction of a particle is given by

where A and B are constants. Show that this wavefunction is (a) a solution to the time independent Schroedinger equation, assuming that the particle is free, i.e. no force on it, zero potential energy for all positions) and (b) find the corresponding total energy, E, of the particle.

 

5. What is the minimum energy of (a) a proton and (b) an alpha particle trapped in a one-dimensional region the size of a uranium nucleus, radius  = 7 10-15 m?

 

 

 

 

Please note that what appeared as first homework from last year, i.e.: Serway chapter 7, problem 4; 

chapter 8, problem 2 will be set at some later point in time

 

 

 

Homework: due Tues, Jan 29

 

1. A 0.1 mA electron beam with kinetic energy 54 V enters a sharply defined region of lower potential where the kinetic energy of the electron is increased by 10 eV. What current is reflected at the boundary? (This simulates electron scattering at normal incidence from a metal surface, as in the Davisson-Germer experiment.

 

2. Find an equation for the difference between adjacent energy levels (ΔEn = E n+1 - En for the infinite square-well potential. Calculate ΔE1, ΔE8, and ΔE800 .

 

3. What is the energy level difference between adjacent energy levels (ΔEn = E n+1 - En for the simple harmonic oscillator? What is ΔE0, ΔE2, and ΔE50 ?

1. Consider the step potential of example 7.4 in Serway, page 237, for the case E > U. (a) Examine the Schroedinger equation to the left of the step to find the form of the solution in the range x < 0. Do the same to the right of the step to obtain the solution form for x > 0. Complete the solution by enforcing whatever boundary and matching conditions may be necessary. (b) Obtain an expression for the reflection coefficient R in this case, and show that it can be written in the form

 

 

where k1 and k2 are wavenumbers for the incident and transmitted waves, respectively. Also write an expression for the transmission factor T using the sum rule obeyed by these coefficients. Evaluate R and T in the limiting case of E approaching U and E approaching infinity. Are the results sensible? Explain. This situation is analogous to the partial reflection and transmission of light striking an interface separating two different media.  *Worth 10 points in total.)

 

 

2. the problem from last week again a little bit rephrases: A 0.1 mA electron beam with kinetic energy of 54 eV (i.e. an electron that was accelerated by a potential of 54 V) enters a sharply defined region of lower potential where the kinetic energy of the electron is increased by 10 eV. What current is reflected at the boundary? (This simulates electron scattering at normal incidence from a metal surface, as in the Davisson-Germer experiment.) (Worth 5 points, if you can solve problem 1 this is going to be straightforward. look up how a current is defined, what the unit Ampere really means for a better understanding, recall that any time a wave hits “something”, there will be secondary spherical waves, so it is completely reasonable that a part of the wave should be reflected back, one gets the same insight if one argues abstract mathematically, …, not too hard a problem after all)

 

3. Find the energies of the second, third, fourth, and fifth levels for the three-dimensional cubical box. Which are degenerate?

 

February 12, Midterm. 10:00 to 10:55, then 5 minutes break and another lecture

 

Chapter 6: Quantum Mechanics in three dimensions

 

lecture manuscript for chapter 6/tunneling phenomena can be downloaded here

1. A single electron and a single proton with the same (non-relativistic) total energy approach (in two subsequent single particle experiments) a finite widths potential barrier whose height U is greater than E.

Do they have the same probability of getting through? If not, which of these two particles has the greater tunneling probability? On which parameters of the problem does the tunneling probability actually depend? Does the situation change if the potential energy barrier becomes infinitely wide?

Do these two particles have the same reflection probability? If not, which of these two particles has the greater reflection probability? On which parameters of the problem does the reflection probability actually depend? Does the situation change if the height of the potential energy barrier U is reduced to a value below the total energy of the particles.

Does the situation change if the potential energy barrier becomes infinitely wide?

 

10 points in total since it is a bit involved

 

2. List all possible quantum numbers (n, l, ml) for the n = 6 level in atomic hydrogen.

 

5 points

 

 

 

Electron spin and exclusion principle, the keys to understanding atoms with more than one electron,

 

Chapter 7: Atomic Structure / Many Electron Atoms Atomic structure, Periodic table of elements, X-ray spectroscopy

 

part 1 of lecture manuscript for chapter 7 can be downloaded/printed here

 

part 2 of lecture manuscript for chapter 7 can be downloaded/printed here

 

part 3 of lecture manuscript for chapter 7 can be downloaded/printed here

 

 

 

 

What are the angles between L and the z-axis for orbital quantum number l = 1?  For l = 2?

 

The average value for r for a 1s electron in a hydrogen atom is 1.5 ao. Verify this by calculating the respective expectation value for r.

 

A hydrogen atom is in the 4p state. To what state or states can it go by radiating a photon in an allowed transition?

 

X-ray and Auger spectra, starting with statistical physics

we do some solid state physics, thermal and electrical conductivity to leave the very large subfield of condensed matter physics with superconductivity

 

it’s something quite surprising, discovered by accident, a student fell asleep and did not do what he was paid for, a senior researcher got a crucial insight from the student not doing his job, the boss got a Nobel prize,

 

there have already 4 Nobel prizes been awarded in this field, whoever comes up with the correct theory of type II superconductor may be the next in line to receive such a prize

 

The phenomenon can only be understood by quantum mechanics, in short two fermions couple to become a boson and then most of the electron pairs go into a super state that is at the lowest possible energy level, i.e. can’t loose any energy by scattering, so these Cooper pairs do simply not scatter and flow with zero resistance

 

So here is the link in *.pdf, I do not have it in word as a colleague has given it to me

The respective section in Beiser’s book is 10.9 and 10.10

 

remember electrons are fermions

lecture manuscript for chapter 8 can be downloaded/printed here

 

 

lecture manuscript for superconductivity (in Beiser within the chapter on solid state physics) can be downloaded/printed here

 

lecture manuscript for chapter 8/multi electron atoms can be downloaded here

 

 

 

 

statistical physics part II can be downloaded/printed here , applications of statistical physics to electrical and thermal conductivity can be downloaded/printed here

 

lecture manuscript for chapter 9, part I (Beiser) Statistical Mechanics can be downloaded/printed here

 

new set of homeworks:

Which electronic configuration has the lower energy: [Ar]3d44s2 or [Ar]3d55a1? Identify this element and discuss Hund’s rule in this case. (Note: The notation [Ar] represents the filled configuration for Ar.)

 

Calcium is an element that exhibits the normal Zeeman effect. The difference between adjacent components of the spectral lines is observed to be 0.013 nm for λ = 422.7 nm when calcium is placed in a magnetic field of 1.5 T. From these data calculate “the experimental value of ” and compare it to  the accepted value of today.

 

The effective charge experienced by an M (n=3) electron in an atom of atomic number Z is about (Z-7.4)e. Show that the frequency of the Lα x-rays of such an element is given by 5cR(Z-7.4)2 / 36.

 

 

 

Sodium is a monovalent metal having a density of 0.971 g cm-3, an atomic weight of 23 g mol-1, and an electric resistivity of 4.2 micro-Ohm cm at room temperature. Use this information to calculate (a) the free electron density (b) the Fermi velocity (c) the average time between electron-ion collisions (d) the mean free path of the electrons and (e) the thermal conductivity.

Determine the ratio of the mean free path you calculated to the nearest neighbor distance in sodium, i.e. 0.372 nm.  10 points in total as it is a bit involved and requires that you go carefully to the lecture notes.

 

Prove that a dimensionless number results from this formulae

 

 

 

what does this formulae represent?

 

on the basis of this formulae discuss when Maxwell-Boltzmann statistics is applicable?

 

 

 

 Bits and pieces of nuclear physics for the rest of this quarter

Homeworks: Samuelson Paper: answer these questions concisely, due on the day of the final exam

Samuelson Paper

For the paper itself click

review paper by Lars Samuelson , you need the free abode *.pdf reader to read and print out the paper

 

 

What are Zhores Alferov and Herbert Kroemer are exactly credited for?        2 points

 

Why are quantum dots sometimes called artificial atoms?    2 points

 

 

How does one construct a potential energy barrier in a semiconductor?   2 points

 

 

How does the tunneling probability through a barrier depends on the thickness of the barrier?    2 points

 

 

With what method was the image at the cover of the article taken? Hint compare to Fig. 8 in the article.  2 point

 

 

Chapter 13: Nuclear Structure

Last set of homework problems for this course

 

Ordinary boron is a mixture of the and isotopes and has a composite mass of 10.82 u. What percentage of each isotope is present in ordinary boron?

 

Show that the nuclear density of is over 10 14 times greater than its atomic density. Assume the atom to have the radius of the first Bohr orbit.

 

Find the binding energy per nucleon in  and in .

 

 

Chapter 14: Nuclear decays, radioactivity and reactions

 

 

 

 

 

 

 

 

Lecture manuscript for first part of chapter 13/14 is here

Lecture manuscript second part of chapter 13/14 is here

 

 

 

 

Final exam on March 18st 10:15 – 12:05

Grades available by the end of the week

 

 

If you didn’t get an A this time, do not worry so much, I didn’t get straight As all my live and neither did Heisenberg, if you want to know how badly he “screwed up” his final PhD exam, click here, nevertheless he was a professor at age 25 and one of the greatest physicists ever

 

 

 

 

 

 

 

 

 

 

 

 

 

Two (W. PauLi and N. Bohr) dignitaries having fun playing and contemplating a spinning top

 

 Have a Look at the square of a wave function, these guys do really exist !

http://www.amherst.edu/~ermace/sth/sth.html

 

 

 

 

Stonehenge “in stone”, the observatory/place of Druid Worship in England from about 1900 B.C.

(that some scholars believe was build by German immigrants)

 from the 2003 review paper by Lars Samuelson mentioned above,

by the end of the course you will understand that it is actually a sketch of state-of-the-art nanotechnology that will work on the basis of quantum mechanics, the little colored marbles representing atoms of the III and V column of the periodic table and the “dome” being gold  

 

Quantum dot henge

“in semiconductors”

 

 

 

 

 

There will also be opportunities to do undergraduate research

 

 

 

 

 

 

 

http://www.physics.pdx.edu/~girish/312-questions/

 

 

from the author’s of Physics for Poets, mentioned above, after word: To be human is to wonder … The baby is displayed behind glass, well-scrubbed, and one need not know about the delivery room (it is soundproofed). Thus we are spared the agony of wonder, which is not unlike love and makes as little (or as much) sense as love. 

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an after thought