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8.05

Quantum Physics II

5-0-7 units · Undergraduate

Vector spaces, linear operators, and matrix representations. Inner products and adjoint operators. Commutator identities. Dirac's Bra-kets. Uncertainty principle and energy-time version. Spectral theorem and complete set of commuting observables. Schrodinger and Heisenberg pictures. Axioms of quantum mechanics. Coherent states and nuclear magnetic resonance. Multiparticle states and tensor products. Quantum teleportation, EPR and Bell inequalities. Angular momentum and central potentials. Addition of angular momentum. Density matrices, pure and mixed states, decoherence.

Fall 2013

Topics

  • Wave Mechanics
  • Spin One-half, Bras, Kets, and Operators
  • Linear Algebra: Vector Spaces and Operators
  • Dirac’s Bra and Ket Notation
  • Uncertainty Principle and Compatible Observables
  • Quantum Dynamics
  • Two State Systems
  • Multiparticle States and Tensor Products
  • Angular Momentum
  • Addition of Angular Momentum

Readings

  • Griffiths, David J. Introduction to Quantum Mechanics . 2nd ed. Pearson Prentice Hall, 2004. ISBN: 9780131118928.
    Required
  • Shankar, Ramamurti. Principles of Quantum Mechanics . 2nd ed. Plenum Press, 1994. ISBN: 9780306447907.
    Required
  • Cohen-Tannoudji, Claude. Quantum Mechanics . 2 vols. Wiley, 2006. ISBN: 9780471164326. (Useful for 8.05 and 8.06: Some students find it too encyclopedic.)
    Listed reading
  • Dirac, P. A. M. The Principles of Quantum Mechanics . 4th ed. Oxford at the Clarendon Press, 1958. (Quantum mechanics from the Master. Deep, hard and rewarding to read, but probably in the summer.)
    Listed reading
  • Feynman, R. P. Feynman Lectures On Physics . Vol. 3. Addison Wesley Longman, 1970. ISBN: 9780201021158. (Ch. 6 on spin and Ch. 9 on the ammonia maser are particularly useful.)
    Listed reading
  • Ohanian, Hans. Principles of Quantum Mechanics . Prentice Hall, 1989. ISBN: 9780137127955. (More emphasis than Griffiths on operator methods but less depth on some other topics.)
    Listed reading
  • Sakurai, J. J. Modern Quantum Mechanics . Addison-Wesley Pub., 1993. ISBN: 9780201539295. (A revision of the text by Sakurai. Advanced for 8.05.)
    Listed reading
  • Axler, Sheldon. Linear Algebra Done Right . 2nd ed. Springer, 1997. ISBN: 9780387982595. (A conceptual introduction to vector spaces and linear operators.)
    Listed reading
  • [Griffiths] = Griffiths, David J. Introduction to Quantum Mechanics . 2nd ed. Pearson Prentice Hall, 2004. ISBN: 9780131118928.
    Required
  • [Shankar] = Shankar, Ramamurti. Principles of Quantum Mechanics . 2nd ed. Plenum Press, 1994. ISBN: 9780306447907.
    Required
  • [Ohanian] = Ohanian, Hans. Principles of Quantum Mechanics . Prentice Hall, 1989. ISBN: 9780137127955. (More emphasis than Griffiths on operator methods but less depth on some other topics.)
    Listed reading
  • [Shankar] Chapter 1.
    Listed reading
  • [Griffiths] Chapter 3.
    Listed reading
  • [Shankar] Chapter 9.
    Listed reading
  • For further reading on angular momentum with more emphasis on operators than Griffiths, you should consult one or more of the following: [Ohanian] Chapter 7. [Shankar] Section 12.5.
    Listed reading

Prerequisites & course information

Prereq: 8.04 or 8.041 U (Fall) 5-0-7 units Credit cannot also be received for 8.051

Sources