Massachusetts Institute of Technology

Department of Physics

Physics 8.04 March 13, 1997

Quantum Physics I, Spring 1997

Problem Set 5

(Due Friday, March 21 at 5:00 pm sharp.)

Agenda and required readings for the weeks of March 17:

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.

• L11, 03/18: Normalization, Parseval's Theorem, Hermitian Inner Product; Averages and Operators, Pure States and Operators
  Readings: CN ``Quantum Averages and Operators'', G 46-48, 55-64
• L12, 03/20: Quantum Dynamics, Movies of Wave Functions, Proof of F=ma, Conservation Laws
  Readings: RH CN ``General Features of the Time Dependent Schrödinger Equation (TDSE),'' G 41-45, 125-128

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

• Contents
• List of Figures
• Derivation of Operators from the de Broglie Hypothesis (25 pts)
  • Completing the basic set from lecture
  • Powers of x and p
  • Arbitrary functions of x and p
  • Beyond one dimension
  • Hamiltonian operators
• Application of Operators (25 pts)
  • Normalization
  • Probability distributions
  • Expectations
  • Uncertainties
  • Pure states of energy
• Particle Trapped in a Cavity Revisited (25 pts)
  • Wave function
  • Momentum Distribution
  • Heisenberg Uncertainty Principle in Action
• Uncertainty Principle (25 pts)
  • Shift away the mean values
  • Generate an inequality
  • Separation of the terms
  • Two general uncertainty principles
  • Application to x and p
• About this document ...

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