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Quantum mechanics is one of the foundations of modern physics and provides a general scheme for understanding a vast range of physical phenomena. Every physicist needs to be familiar with the main ideas and results of quantum mechanics and a majority use it, in some form, on a daily basis. This course aims to give you a solid understanding of the ground rules of quantum mechanics as well as it applications.
Quantum mechanics is tremendously important in our modern lifestyle; it provides an understanding of the operations of semiconductors, lasers, magnetic resonance and a variety of other technologies that were inconceivable before the development of the subject. It has also profoundly changed our view of the physical world. Nearly 80 years after quantum mechanics was formalized, experts are still able to unearth apparent paradoxes within the theory and dispute their implications.
In Phys 332, the general rules of quantum mechanics will be described in terms of the state representation framework rather than the more limited wavefunction approach. Much of this will be illustrated using two-state quantum systems, which have no classical counterparts but capture the essential ideas of the subject without the distracting mathematical complications associated with single particles with a position degree of freedom. The general rules will then be applied to such systems with emphasis on the harmonic oscillator and the hydrogen atom.
Course Number: PHYS 332-01
Instructor:
Prof. David Collins, Physics Department
252 Olin Hall
Telephone: 577-3636
Email: dcollins@bucknell.edu
Class Times: MWF 10:00-10:52am
Classroom: Olin 264
First Class Meeting: Wednesday 25 August 2004.
Prerequisites: PHYS 221, PHYS 222 and MATH 212
Text: J. S. Townsend, A Modern Approach to Quantum Mechanics, University Science Books, Sausalito, CA (2000).
First Day Handout: Postscript Format Pdf Format
Outline: Postscript Format Pdf Format
Syllabus: The following is subject to change.
- Spin half systems and Stern-Gerlach type experiments.
- State representation, measurements and time evolution for spin half and analogous systems.
- General framework of quantum mechanics.
- Particles in one dimension: wave mechanics.
- One dimensional harmonic oscillator.
- Rotations and angular momentum.
- Particles in central potentials, hydrogen atom.
- Time-independent perturbation theory.
- Quantum foundations and information.
Homework Solutions
Homework solutions will be posted on ISR's electronic reserves system (Eres). Transfer to the course Eres page.
There will be two class exams on Monday 21 February 2005 and Monday 4 April 2005. There will be a comprehensive final exam on a date to be announced by the registrar.
Exams from previous years.
General Texts
In your freshman and sophomore level courses you probably never had to consult more than one text per course. You'll now learn that 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 Bertrand library. Texts which are indicated in red are on reserve in the Bertrand library.
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.
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.
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.
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.
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.
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.
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 text. 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.
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.
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.
- 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).
- A. Zeilinger, "Experiment and the foundations of quantum physics", Rev. Mod. Phys. 71 288-297 (1999).
- A. Aspect, "Experimental Test of Bell's Inequalities Using Time- Varying Analyzers", Phys. Rev. Lett. 49 1804 (1982).
Particle Diffraction and Electron Microscopy
- Physics Web Excellent summary of experimental efforts to demonstrate interference and diffraction of particles passing through single and multiple slits. From Physics World.
- Electron interference patterns from LAMEL, Bologna, Italy.
- Electron interference patterns from Hitachi, Japan.
- A Zeilinger, R Gähler, C G Shull, W Treimer and W Mampe, "Single- and double-slit diffraction of neutrons," Rev. Mod. Phys. 60, 1067 (1988).
- Electron scattering Electron scattering and microscopy images from USC, Materials Sciences.
- Electron scattering Electron scattering images from ETH Zurich, Switzerland.
- 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.
- Electron microscopy: Assorted images from the Biology Department, Wake Forest University.
- Electron microscopy: Assorted images from the Electron Microscope Unit, University of Cape Town, South Africa.
Atomic and Molecular Spectra
- Experimental Observations for Hg, He and N2 From Georgia State University
- Spectroscopy in Astronomy From Harvard.
- Hydrogen Spectrum From IMSA.
Classical Mechanics
- Classical harmonic oscillator From Michigan State University.
One Dimensional Quantum Mechanics
- One dimensional quantum system simulator From Paul Falstad.
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