Course Description

Phys 422 is a continuation of Phys 321, Quantum Theory I, which covered the basic framework and some fundamental tools of quantum mechanics. In Quantum Theory II, this framework will be applied to various widely encountered physical situations and additional tools will be developed. The material which will be covered is more than just a set of situation specific topics and applications. Many of the new concepts and techniques that you will learn are useful in a diverse array of physical situations.

Course Number: PHYS 422

Instructor: Prof. David Collins, Physics

Contact Information:

Class Times: TTh 11:00am - 12:15pm

Classroom: Medesy 180

First Class Meeting: Tuesday 23 January 2007

Prerequisites: PHYS 321

Text:

J. S. Townsend, A Modern Approach to Quantum Mechanics, University Science Books, Sausalito, CA (2000).

First Day Handout: Pdf Format

Outline: Pdf Format

Syllabus

The following is subject to change.

  1. Review of the framework of quantum mechanics.
  2. Hydrogen atom energy levels.
  3. Evolution under time dependent potentials: spin 1/2 systems.
  4. Time-independent perturbation theory.
  5. Fine structure of the hydrogen atom.
  6. Scattering.
  7. Systems of more than one particle, entanglement.
  8. Identical particles.
  9. Quantum foundations and information.

Homework Assignments

Homework 1 Due: 29 Jan 2007 Pdf
Homework 2 Due: 6 Feb 2007 Pdf
Homework 3 Due: 13 Feb 2007 Pdf
Homework 4 Due: 27 Feb 2007 Pdf
Homework 5 Due: 20 Mar 2007 Pdf
Homework 6 Due: 27 Mar 2007 Pdf
Homework 7 Due: 5 April 2007 Pdf
Homework 8 Due: 12 April 2007 Pdf
Homework 9 Due: 26 April 2007 Pdf
Homework 10 Due: 3 May 2007 Pdf
Homework 11 Due: 10 May 2007 Pdf

Homework Solutions

Homework solutions will be posted at H:\DOWNLOAD\dacollin\2007Spring\Phys422\homework.

Exams

There will be two hour long exams during class on the following dates Tuesday 6 March 2007 and Tuesday 17 April 2007. There will be a comprehensive final exam on Tuesday 15 May 2007.

Exam Solutions.

Semester Exam
Spring 2007 Class exam 1: Solutions Pdf
Spring 2007 Class exam 2: Solutions Pdf


Supplementary Reading

In your freshman and sophomore level courses you probably never had to consult more than one text per course. This is the exception. There is no single text which is completely suitable for this course and you will find that you may have to consult several to develop an understanding of the course material. The following list is a starting point; there are many other possible texts available in the library.

  1. General Texts

    1. R. P. Feynman, R. B. Leighton and M. Sands, Lectures on Physics, Vol III, Addison-Wesley (1965).

      The first chapter of Vol III of Feynman's lectures still contains one of the best introductions to quantum mechanics. This is essential reading for anyone interested in the subject. The are several chapters which include comprehensive discussions of spin half and other discrete quantum systems at a level suitable for this course.

    2. D. J. Griffiths, Introduction to Quantum Mechanics, Prentice-Hall (1995).

      Possibly the most accessible quantum mechanics text at this level. Generally very well written and easy to read. However, this text focuses almost exclusively on wave mechanics and there is little actual use of the Dirac formalism. Somewhat limited in it's discussion of time evolution of quantum systems.

    3. J. J. Sakurai, Modern Quantum Mechanics, Prentice-Hall (1995).

      An excellent text which uses two state systems to introduce many key features of quantum mechanics. This may be a little challenging to read but it develops the subject in a manner similar to that of this course.

    4. R. Shankar, Principles of Quantum Mechanics, Plenum (1980).

      An excellent comprehensive text which is very systematic and covers many topics. Although it emphasizes the physics of particles moving in one or more dimensions, there is adequate coverage of spin half and other discrete quantum systems. The presentation of the main axioms is sufficiently general. This may also be a little challenging to read - I don't expect you to be able to read the chapter on Langrangian Mechanics (Ch 2) but the book is written so that you can skip this.

    5. C. Cohen-Tannoudji, B. Diu and F. Laloe, Quantum Mechanics, John Wiley (1977).

      Encyclopedic compendium of all things quantum mechanical, circa 1977. This two volume set is dense, often quite heavy mathematically and has an initially bewildering indexing system, but it covers a vast array of quantum mechanical topics in great details and features numerous interesting examples. One of the few texts to discuss topics like two-state systems, tensor products, etc..., in adequate detail. If you are going to do more than one course in quantum mechanics in your graduate career, this is an essential text.

    6. D. Bohm, Quantum Theory, Dover (1979).

      "Old school" classic written in 1951 by one of the leading experts in quantum mechanics. Comprehensive coverage of wave mechanics, albeit with an archaic notation. This contains many important examples worked out in great detail as well as thorough discussions of the key experiments that led to the development of quantum mechanics. Added bonus: it's a Dover publication and you should be able to buy it for less than $20.

    7. T. F. Jordan, Quantum Mechanics in Simple Matrix Form, Wiley (1986).

      This is one of the few introductory level texts which describes spin-half systems in detail. However, its treatment of the subject is quite mathematical and idiosyncratic; the state vector is never introduced and the statistics of measurement outcomes are described entirely in terms of algebraic properties of appropriate matrices. By doing this one can avoid the pitfalls of associating a reality with or interpreting the state vector and have the measurements occupy center stage. For example, for spin-half systems, matrices associated with spin components square to a positive scalar multiple of the identity. Evidently one can then conclude that the spin component has values plus or minus the square root of the scalar multiple. Following this one can demonstrate the usual features of measurements associated with these systems. The connection between these matrices and the results of measurements is never really precisely spelled out. A more conventional formalism that is like this would use the notion of density operators and eigenvalues of observables.

      If you are still confused on the basics of complex numbers, linear algebra or probabilities, the first six (short) chapters should be a great help.

    8. G. Greenstein and A. G. Zajonc, The Quantum Challenge, Jones and Bartlett (1997).

      Most undergraduate texts barely touch on the truly fundamental aspects of quantum mechanics. These include issues such as interpretations of quantum state and measurements, non-locality and entangled states. This text is an excellent overview of theoretical and experimental developments in the foundations of quantum mechanics intended for an undergraduate audience. The chapter on the evidence for photons is particularly informative. (Note: a second edition is due for publication in late 2005).

    9. A. Peres, Quantum Theory: Concept and Methods, Kluwer (1995).

      What is an entangled state? What is the meaning of a density matrix? How much information is contained in a quantum state? What is Bell's theorem? If issues at the foundation of quantum mechanics interest you, then you should read this. This is definitely an advanced text and not the place to learn about hydrogen atom wavefunctions. However, it is the single best book on topics like these, many of which intersect strongly with current research in quantum information.

    10. R. B. Griffiths, Consistent Quantum Theory, Cambridge (2002).

      If issues such as the Schrodinger cat paradox, collapse of the wavefunction and action at a distance bother you then you should investigate the consistent histories approach to quantum mechanics. This is an interpretation, developed by Bob Griffiths and others, which avoids such paradoxes. This is an advanced text which lays out the approach in clear detail.

Links and Animations

  1. Animations
    1. Classical harmonic oscillator. From Michigan State University.
    2. One dimensional quantum system simulator. From Paul Falstad.
    3. Stern-Gerlach simulator. Developed by Dan Schroeder, Weber State University. Now hosted by Oregon State University.
  2. Experimental Investigations of the Foundations of Quantum Physics

      The basic ideas of quantum mechanics are frequently presented in the form of thought experiments. In this course we have used sequences of imaginary Stern-Gerlach experiments on spin 1/2 systems to illustrate the fundamental physical and mathematical concepts of quantum mechanics. Such sequences of Stern-Gerlach experiments have never actually been performed. So what is the evidence for the physics we describe in the classroom? Mostly it emanates from equivalent experiments in quantum optics. Here are some references.

    1. J. M. Raimond, M. Brune, and S. Haroche, "Colloquium: Manipulating quantum entanglement with atoms and photons in a cavity," Rev. Mod. Phys. 73 565 (2001).
    2. A. Zeilinger, "Experiment and the foundations of quantum physics", Rev. Mod. Phys. 71 288-297 (1999).
    3. A. Aspect, "Experimental Test of Bell's Inequalities Using Time- Varying Analyzers", Phys. Rev. Lett. 49 1804 (1982).
    4. Photon Quantum Mechanics Undergraduate level laboratories developed at Colgate University. Links to several articles describing experiments.
    5. Modern Quantum Mechanics Experiments for Undergraduates Undergraduate level laboratories developed by Mark Beck at Whitman College. Links to several articles describing experiments.

      6. Some of experiments illustrating fundamental aspects of quantum mechanics have also been demonstrated using intereference of neutron beams. Such neutron interferometry experiments have been carried out since the 1970s.

    6. Daniel M. Greenberger, "The neutron interferometer as a device for illustrating the strange behavior of quantum systems," Rev. Mod. Phys. 55, 875 (1983).
    7. J.-L. Staudenmann, S. A. Werner, R. Colella, and A. W. Overhauser, "Gravity and inertia in quantum mechanics," Phys. Rev. A 21, 1419 (1980).
    8. S. A. Werner, R. Colella, A. W. Overhauser, and C. F. Eagen, "Observation of the Phase Shift of a Neutron Due to Precession in a Magnetic Field," Phys. Rev. Lett. 35, 1053 (1975).
    9. H. Rauch and W. Treimer, and U. Bonse, "Test of a single crystal neutron interferometer," Phys. Lett. A 47, 369-71 (1974).

      10. There have been several demonstrations of the delayed-choice experiment. These articles are intended for a specialist audience. However, you should be able to understand the description of the conventional delayed choice experiment in the introduction, experimental setup and experimental results sections of Hellmuth, et.al. There is a good discussion of the delayed choice experiment in "The Quantum Challenge" by Greenstein and Zajonc.

    10. T. Hellmuth, H. Walther, A. Zajonc, and W. Schleich, "Delayed-choice experiments in quantum interference," Phys. Rev. A 35, 2532-40 (1987).
    11. B. J. Lawson-Daku, R. Asimov, O. Gorceix, Ch. Miniatura, J. Robert, and J. Baudon, "Delayed choices in atom Stern-Gerlach interferometry," Phys. Rev. A 54, 5042 (1996).
    12. Yoon-Ho Kim, Rong Yu, Sergei P. Kulik, Yanhua Shih, and Marlan O. Scully, "Delayed "Choice" Quantum Eraser," Phys. Rev. Lett. 84, 1-5 (2000).
  3. Stern-Gerlach experiment
    1. Stern-Gerlach brownies. Chefs: Carrie Nugent and Adam Cohen.
    2. "Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld," W. Gerlach und O. Stern, Zeitschrift fur Physik 9, 349-352 (1922). "Über die Richtungsquantelung im Magnetfeld," W. Gerlach und O. Stern, Annalen der Physik, 74, 673-699 (1924). The original articles are in German, but both of these contain prints of the photographic target plate. Copies are available here.
    3. Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics Physics Today 56, 53 (Dec 2003). Review of the history of the Stern-Gerlach experiment.
  4. Particle Diffraction Experiments
    1. Physics Web Excellent summary of experimental efforts to demonstrate interference and diffraction of particles passing through single and multiple slits. From Physics World.
    2. Electron interference patterns from LAMEL, Bologna, Italy.
    3. Electron interference patterns from Hitachi, Japan.
    4. A Zeilinger, R Gahler, C G Shull, W Treimer and W Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067 (1988).
    5. C. Shull, "Single-Slit Diffraction of Neutrons," Phys. Rev. 179, 752 (1969). Beautiful demonstration of single slit electron diffraction. You could verify that the uncertainty principle from these results too!
    6. Electron scattering Electron scattering and microscopy images from USC, Materials Sciences.
    7. Electron scattering Electron scattering images from ETH Zurich, Switzerland.
    8. Electron microscopy: Pfisteria dinoflagellates, which are responsible for fish kills in estuaries in North Carolina. From Center for Applied Aquatic Ecology, North Carolina State University.
    9. Electron microscopy: Assorted images from the Biology Department, Wake Forest University.
    10. Electron microscopy: Assorted images from the Electron Microscope Unit, University of Cape Town, South Africa.
  5. Uncertainty Principle
    1. O. Nairz, M. Arndt, and A. Zeilinger, "Experimental verification of the Heisenberg uncertainty principle for fullerene molecules," Phys. Rev. A 66, 032109 (2002). Demonstration of the uncertainty principle in large molecules.
  6. One Dimensional Quantum Mechanics
    1. One dimensional quantum system simulator From Paul Falstad.
    2. GaAs quantum dot. Quantum dot with confinement produced by metallic gates. From Christian Schonenberger, University of Basel.
    3. Metallic island SET. Single electron transistor. From K. Matsumoto, Stanford University
    4. STM images from IBM's Almaden research center. Highly recommended.
  7. Quantum Information and Quantum Computation
    1. Toshiba's quantum information group. Toshiba have developed a prototype for commercial quantum crytography.
    2. MagiQ MagiQ is a company devoted to building quantum information processing devices. They now offer a commercial quantum cryptography device.
    3. idQuantique idQuantique builds various quantum information processing devices. They also offer a commercial quantum key distribution (quantum cryptography) device.

This page is maintained by David Collins
Last modified: 13 March 2007