Massachusetts Institute of Technology

Department of Physics

Physics 8.04 March 20, 1997

Quantum Physics I, Spring 1997

Problem Set 6

(Due Friday, April 4 at 5:00 pm sharp.)

Agenda and required readings for the weeks of March 31:

The abbreviations are RH = Resnick and Halliday (section numbers), G = Gasiorowicz (section(s) contained within the given range of pages), H = Heisenberg (section numbers), FT = French and Taylor (section numbers), CN = class notes provided on the web.

• L13, 04/01: Conservation Laws in Quantum Dynamics, Proof of F=ma (Ehrenfest's Theorem)
  Readings: CN ``Notes on General Features of the Time Dependent Schrödinger Equation (TDSE)'', G 43-46, 125-128
• L14, 04/03: Separation of Variables, Gaussian Wave Packets, Scattering
  Readings: Section 1 of CN ``Notes on Derivation and Features of the Time Independent Schrödinger Equation (TISE),'' Sections 1-2 of CN ``Notes on Scattering Theory,'' G 30-32, 74-78

Work requested of the students is highlighted by either a question mark (?) or .

• Contents
• Practice with Mathematical Manipulations
  • Hermitian Inner Product
  • Hemiticity of Operators
  • Manipulation of Fourier Integrals
  • Pure States
• Computer Assignment
• A Wave Packet in Simple Harmonic Motion: Coherent State of Simple Harmonic Oscillator
  • Effective equations for A(t), B(t) and C(t)
  • Solutions of constant width
  • Rigid shape of the probability distribution
  • Conservation of probability
  • Correspondence Principle/Ehrenfest's Theorem
  • Connection to Problem 2
• A Wave Packet Moving with Constant Acceleration
  • Apply Ehrenfest's Theorem
    • Generate the equations
    • Solve the equations
    • Interpret your results
  • Full Solution
    • Generate the equations
    • Solve the equations
    • Interpret your results
  • Connection to Problem 2
• About this document ...

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