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8.06

Quantum Physics III

5-0-7 units · Undergraduate

Continuation of 8.05 . Units: natural units, scales of microscopic phenomena, applications. Time-independent approximation methods: degenerate and nondegenerate perturbation theory, variational method, Born-Oppenheimer approximation, applications to atomic and molecular systems. The structure of one- and two-electron atoms: overview, spin-orbit and relativistic corrections, fine structure, variational approximation, screening, Zeeman and Stark effects. Charged particles in a magnetic field: Landau levels and integer quantum hall effect. Scattering: general principles, partial waves, review of one-dimension, low-energy approximations, resonance, Born approximation. Time-dependent perturbation theory. Students research and write a paper on a topic related to the content of 8.05 and 8.06 .

Spring 2018

Topics

  • Time Independent Perturbation Theory
  • Time Independent Perturbation Theory (continued)
  • Degenerate Perturbation Theory
  • Hydrogen Atom Fine Structure
  • Hydrogen Atom Fine Structure (continued)
  • Zeeman Effect and Introduction to the Semiclassical Approximation
  • The Semiclassical WKB Approximation
  • WKB (continued). Airy Functions and Connection Formulae
  • Time Dependent Perturbation Theory
  • Fermi’s Golden Rule
  • Fermi’s Golden Rule for Harmonic Transitions
  • Hydrogen Ionization (completed). Light and Atoms
  • Light and Atoms (continued). Charged Particles in Electromagnetic Fields
  • Charged Particles in Electromagnetic Fields (continued)
  • Adiabatic Approximation
  • Peer Edit Session
  • Adiabatic Approximation (continued)
  • Adiabatic Approximation: Berry’s Phase
  • Adiabatic Approximation: Molecules
  • Scattering
  • Scattering (continued 1)
  • Scattering (continued 2)
  • Scattering (continued 3). Identical Particles
  • Identical Particles (continued 1)
  • Identical Particles (continued 2)

Readings

  • [Griffiths] = Griffiths, David J. and Darrell F. Schroeter. Introduction to Quantum Mechanics . Cambridge, United Kingdom: Cambridge University Press, 2018. ISBN: 9781107189638.
    Required
  • [Cohen-Tannoudji] = Cohen-Tannoudji, Claude, et. al. Quantum Mechanics, Vol. 2 . Wiley, 1991. ISBN: 9780471164357.
    Listed reading
  • [Shankar] = Shankar, Ramamurti. Principles of Quantum Mechanics . Plenum Press, 2011. ISBN: 9780306447907.
    Listed reading
  • [Sakurai] = Sakurai, J. J. Modern Quantum Mechanics . Cambridge University Press, 2017. ISBN: 9781108422413.
    Listed reading
  • [Griffiths] Chapter 6
    Listed reading
  • [Cohen-Tannoudji] Chapter XI
    Listed reading
  • [Shankar] Chapter 17
    Listed reading
  • [Cohen-Tannoudji] Chapter XI and Chapter XII
    Listed reading
  • [Cohen-Tannoudji] Chapter XII
    Listed reading
  • [Griffiths] Chapter 8 on WKB approximation
    Listed reading
  • [Griffiths] Chapter 9
    Listed reading
  • [Cohen-Tannoudji] Chapter XIII and/or [Shankar] Chapter 18
    Listed reading
  • WEEK #: 6 · READING: [No readings]
    Reading assignment
  • WEEK #: 7 · READING: [No readings]
    Reading assignment
  • WEEK #: 8 · READING: [Griffiths] Sections 9.2 and 9.3 for interactions of atoms with light. Chapter 10 for the adiabatic approximation.
    Reading assignment
  • [Cohen-Tannoudji] Chapter VI Complement E, which has a nice treatment of Landau levels.
    Listed reading
  • WEEK #: 10 · READING: [No readings]
    Reading assignment
  • [Griffiths] Chapter 11
    Listed reading
  • [Cohen-Tannoudji] Chapter VIII and/or [Shankar] Chapter 19
    Listed reading
  • WEEK #: 12 · READING: [No readings]
    Reading assignment
  • [Griffiths] Chapter 5
    Listed reading
  • [Shankar] Chapter 10
    Listed reading
  • [Cohen-Tannoudji] Chapter XIV
    Listed reading
  • Griffiths, David J. and Darrell F. Schroeter. Introduction to Quantum Mechanics . Cambridge, United Kingdom: Cambridge University Press, 2018. ISBN: 9781107189638.
    Required
  • Cohen-Tannoudji, Claude, et. al. Quantum Mechanics, Vol. 2 . Wiley, 1991. ISBN: 9780471164357. (Highly recommended) Vol.1. is also good.
    Listed reading
  • Merzbacher, Eugen. Quantum Mechanics . Wiley, 2005. ISBN: 9788126533176. (Highly recommended)
    Listed reading
  • Shankar, Ramamurti. Principles of Quantum Mechanics . Plenum Press, 2011. ISBN: 9780306447907. (Recommended)
    Listed reading
  • Sakurai, J. J. Modern Quantum Mechanics . Cambridge University Press, 2017. ISBN: 9781108422413.
    Listed reading
  • Schumacher, Benjamin, and Michael D. Westmoreland. Quantum Processes, Systems, and Information . Cambridge University Press, 2010. ISBN: 9780521875349.
    Listed reading
  • Feynman, Richard. P. Feynman Lectures On Physics . Vol. 3 . Basic Books, 2011. ISBN: 9780201021158.
    Listed reading
  • Ohanian, Hans. Principles of Quantum Mechanics . Prentice Hall, 1989. ISBN: 9780137127955.
    Listed reading
Spring 2016

8.06 is the third course in the three-sequence physics undergraduate Quantum Mechanics curriculum. By the end of this course, you will be able to interpret and analyze a wide range of quantum mechanical systems using both exact analytic techniques and various approximation methods. This course will introduce some of the important model systems studied in contemporary physics, including two-dimensional electron systems, the fine structure of Hydrogen, lasers, and particle scattering.

Readings

Spring 2005

Topics

  • Natural Units
  • Degenerate Fermi Systems
  • Charged Particles in a Magnetic Field
  • Time-independent Perturbation Theory
  • Variational and Semi-classical Methods
  • The Adiabatic Approximation and Berry’s Phase
  • Scattering
  • Time-dependent Perturbation Theory
  • Quantum Computing

Readings

  • Griffiths, David J. Introduction to Quantum Mechanics . 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2004. ISBN: 9780131118928.
    Listed reading
  • Cohen-Tannoudji, Claude. Quantum Mechanics . 2 vols. New York, NY: Wiley, 1977. ISBN: 9780471164326.
    Listed reading
  • Sakurai, J. J. Modern Quantum Mechanics . Reading, MA: Addison-Wesley Pub., 1994. ISBN: 9780201539295.
    Listed reading
  • Shankar, Ramamurti. Principles of Quantum Mechanics . 2nd ed. New York, NY: Plenum Press, 1994. ISBN: 9780306447907.
    Listed reading
  • Griffiths, chapter 5.3
    Listed reading
  • Cohen-Tannoudji, chapter XI Complement F
    Listed reading
  • Cohen-Tannoudji, chapter VI Complement E
    Listed reading
  • Griffiths, chapter 6
    Listed reading
  • Cohen-Tannoudji, chapter XI including Complements A-D
    Listed reading
  • Cohen-Tannoudji, chapter XII
    Listed reading
  • See also Shankar, chapter 17 and Sakurai, chapter 5.1-3
    Listed reading
  • Griffiths, chapters 7, 8
    Listed reading
  • Cohen-Tannoudji, chapter XI Complements E, F, G
    Listed reading
  • See also Shankar, chapter 16 and Sakurai, chapter 5.4
    Listed reading
  • LEC #: 16-18 · TOPICS: The Adiabatic Approximation and Berry’s Phase · READINGS: Griffiths, chapter 10
    Reading assignment
  • Griffiths, chapter 11
    Listed reading
  • Cohen-Tannoudji, chapter VIII
    Listed reading
  • See also Shankar, chapter 19
    Listed reading
  • Griffiths, chapter 9
    Listed reading
  • Cohen-Tannoudji, chapter XIII
    Listed reading
  • See also Shankar, chapter 18 and Sakurai, chapter 5.5-8
    Listed reading
  • Griffiths, David J. Introduction to Quantum Mechanics . 2nd ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2004. ISBN: 9780131118928. (Required)
    Listed reading
  • Cohen-Tannoudji, Claude. Quantum Mechanics . 2 vols. New York, NY: Wiley, 1977. ISBN: 9780471164326. (Required)
    Listed reading
  • Sakurai, J. J. Modern Quantum Mechanics . Reading, MA: Addison-Wesley Pub., 1994. ISBN: 9780201539295. (Recommended if you like it; somewhat advanced)
    Listed reading
  • Shankar, Ramamurti. Principles of Quantum Mechanics . 2nd ed. New York, NY: Plenum Press, 1994. ISBN: 9780306447907. (Recommended if you like it; somewhat advanced)
    Listed reading
  • Ohanian, Hans. Principles of Quantum Mechanics . Upper Saddle River, NJ: Prentice Hall, 1989. ISBN: 9780137127955.
    Listed reading

Prerequisites & course information

Prereq: 8.05 U (Spring) 5-0-7 units

Sources