Course Description

Physics 222 is an overview of modern physics with a strong emphasis on quantum mechanics and its applications. Quantum mechanics was developed in the early twentieth century in response to several observed phenomena which could not be described by classical physics. This theory successfully solved many outstanding problems, particularly those related to physics at the microscopic level, and currently provides the broadest understanding of the physical world at the most fundamental levels. A majority of physics research activity today involves quantum mechanics in some form. Quantum mechanics is also essential for understanding how lasers, semiconductors, superconductors, nuclear reactors, magnetic resonance, and other devices in daily use, operate. It also gives rise to many apparently bizarre phenomena, which are completely counterintuitive and inexplicable from your everyday classical perspective. Almost a century after its invention, experts still do not agree on the interpretation of such fundamental features as measurement or preparation of a quantum system. If these issues and applications intrigue you, then this course is where you should start.

Quantum mechanics borrows heavily from classical wave mechanics and the first part of the course will be devoted to developing a solid understanding of the theory of classical vibrations and waves. The bulk of the course will be devoted to developing quantum mechanics in a quasi-historical way. This will lead to simple examples of the Schroedinger equation and applications to atomic structure, spectra and angular momentum. Some of the peculiarities at the heart of quantum mechanics will be discussed.

Course Number: PHYS 222-01

Instructor: Prof. David Collins, Physics Department

Contact Information:

Class Times: MWF 1:00 - 1:52pm, Thurs 11:00 - 11:52pm

Classroom: Olin 254

First Class Meeting: Wednesday 19 January 2005.

Prerequisites: (PHYS 212 or PHYS 221) and MATH 211

Texts:

First Day Handout: Postscript Format Pdf Format

Outline:

Syllabus

Classical vibrations and Waves

  1. Motion of single simple harmonic oscillators, complex number representation.
  2. Continuous systems, classical wave equation.
  3. Fourier analysis.
  4. Traveling waves.
  5. Superposition of waves.
  6. Interference and diffraction.

Quantum Physics

  1. Wave and particle properties of light and electromagnetic radiation.
  2. Early models of the nuclear atom.
  3. Wavelike properties of particles, uncertainty principle.
  4. Quantum theory, Schroedinger equation.
  5. Particles in one dimension, quantum tunneling.
  6. Simple harmonic oscillator
  7. Particles in three dimensions, hydrogen atom.
  8. Quantization of angular momentum,spin, applications to atomic and molecular spectra.
  9. Multiple particles, Pauli exclusion principle.
  10. Quantum statistics.

Homework Assignments

Homework 1 Due: 24 Jan 2005 Postscript Pdf
Homework 2 Due: 27 Jan 2005 Postscript Pdf
Homework 3 Due: 31 Jan 2005 Postscript Pdf
Homework 4 Due: 3 Feb 2005 Postscript Pdf
Homework 5 Due: 7 Feb 2005 Postscript Pdf
Homework 6 Due: 10 Feb 2005 Postscript Pdf
Homework 7 Due: 14 Feb 2005 Postscript Pdf
Homework 8 Due: 17 Feb 2005 Postscript Pdf
Homework 9 Due: 28 Feb 2005 Postscript Pdf
Homework 10 Due: 3 Mar 2005 Postscript Pdf
Homework 11 Due: 7 Mar 2005 Postscript Pdf
Homework 12 Due: 10 Mar 2005 Postscript Pdf
Homework 13 Due: 21 Mar 2005 Postscript Pdf
Homework 14 Due: 25 Mar 2005 Postscript Pdf
Homework 15 Due: 31 Mar 2005 Postscript Pdf
Homework 16 Due: 8 April 2005 Postscript Pdf
Homework 17 Due: 13 April 2005 Postscript Pdf
Homework 18 Due: 15 April 2005 Postscript Pdf
Homework 19 Due: 20 April 2005 Postscript Pdf
Homework 20 Due: 22 April 2005 Postscript Pdf
Homework 21 Due: 27 April 2005 Postscript Pdf
Homework 22 Due: 29 April 2005 Postscript Pdf

Homework Solutions

Homework solutions will be posted on ISR's electronic reserves system (Eres). Transfer to the course Eres page.

Exams

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.

Semester Exam
Spring 2004 Class exam 1 Postscript Pdf
Spring 2004 Class exam 2 Postscript Pdf
Spring 2004 Final exam Postscript Pdf

Supplementary Reading

  1. Complex Numbers

    1. P. A. Tipler, Physics for Engineers and Scientists, Vol 1, 5th ed., Freeman (2004).

      Appendix D contains a short review of complex numbers on pages AP 21-23.

    2. R. P. Feynman, R. B. Leighton and M. Sands, Lectures on Physics, Vol I, Addison-Wesley (1965). Chapter 22.

      Does the whole idea of the square root of a negative number bother you? It should bother you exactly as much as the idea of a negative number, or the idea of a rational number. Chapter 22 of Vol I of the Feynman lectures gives an excellent and readable coverage of the ideas behind various number systems.

    3. E. Kreyszig, Advanced Engineering Mathematics, 7th ed., Wiley (1993).

      One of the standard mathematics texts for scientists. In general, beyond the level of this course but the introduction to complex numbers (Ch 12. pages 706-718) is accessible at this level.

    4. G. Polya and G. Latta, Complex Variables, Wiley (1974).

      A fully fledged complex analysis text for scientists and engineers but with a more accessible introduction to complex variables than most competitors. Chapter 1, pages 1-17 is accessible at this level.

  2. Classical Vibrations and Waves

    1. P. A. Tipler, Physics for Engineers and Scientists, Vol 1, 5th ed., Freeman (2004).

      Standard introductory physics text. Chapters 14 to 16 cover vibrations and waves at the freshman level.

    2. F. S. Crawford, Jr, Waves, McGraw-Hill (1968).

      Volume III of the Berkeley physics course. End of chapter problems include "at-home" experiments and applications to then current physics.

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

      Excellent and classic lecture series on basic physics by one of the twentieth century's most eminent physicists. Feynman's lectures frequently take a non-standard approach when developing well established aspects of physics but they almost always offer insights far beyond those of standard texts. Chapters 21 to 24 deal with vibrations and oscillations. Chapters 47 to 51 describe waves.

  3. Quantum Physics

    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. A. Beiser, 6th ed., Concepts of Modern Physics, McGraw-Hill (2003).

      Similar coverage and format to Tipler and Llewellyn, although mathematically at a more elementary level.

Links and Animations

  1. Simple Harmonic Motion
    1. Suspended spring-mass system.(Walter Fendt) Mozilla compatible
    2. Suspended spring-mass system.(Walter Fendt) IE compatible
    3. Simple harmonic motion.(Michigan State University) Clear and simple to use.
    4. SHM and rotations. (Davidson College, North Carolina A and T University).
    5. General SHM. (Daniel Roth) Includes damping.
  2. Continuous Oscillations, Waves
    1. Loaded string (From Paul Falstad) String with variable loads.
    2. Transverse standing waves (From J.T. Ng) Standing waves on a string.
    3. Transverse traveling waves (From J.T. Ng) Transverse traveling waves on a string.
  3. Superpositions of Waves
    1. Rectangular and Triangular Waves From Zona Land. Best with IE.
    2. Sinusoidal Waves From Zona Land. Best with IE.
    3. Two dimensional waves; ripple tank (From Paul Falstad) Best with IE.
  4. Interferometry
    1. Michelson interferometer. Animation from Tim McIntyre.
  5. Diffraction
    1. Poisson spot. From N. R. Kolb, University of Saskatchewan.
    2. Poisson spot. From the University of Melbourne.
    3. X-ray diffraction patterns. From Greg Beaucage, Chemical and Materials Engineering, University of Cincinnati.
  6. Atomic Spectra
    1. Experimental Observations for Hg, He and N2 From Georgia State University
    2. Spectroscopy in Astronomy From Harvard.
    3. Hydrogen Spectrum From IMSA.
    4. Zeeman effect. A copy of the article announcing the discovery of the Zeeman effect.
  7. 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.
  8. 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.
  9. 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.
  10. Trapped Ions
    1. University of Michigan TIQC. Chris Monroe's trapped ion research page.
    2. NIST Ion Storage Group.
  11. Harmonic Oscillators
    1. A. Gaidarzhy, G. Zolfagharkhani, R. L. Badzey, and P. Mohanty, "Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators," Phys. Rev. Lett. 94 030402 (2005). Possibly the first experimental demonstration of quantum mechanical effects in a macroscopic oscillator -just recently (2005) accomplished!
  12. 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: 18 March 2005