Massachusetts Institute of Technology

Department of Physics

Physics 8.04 March 7, 1997

Quantum Physics I, Spring 1997

Problem Set 4

(Due Friday, March 14 at 5:00 pm sharp.)

Agenda and required readings for the weeks of Feb. 25:

• L8, 03/11: What is a Quantum State? Specification of a Quantum State:
  CN ``Quantum States and Observables,'' Sections 1 and 2
• L9 03/13: Quantum Superposition, Real and Momentum Space Representations of Quantum States, Fourier Analysis
  CN ``Quantum States and Observables,'' Section 3; G Appendix A

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.

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

• Contents
• Quantum States of Photons
  • a)
  • b)
  • c)
  • d)
• Fourier Transforms: The Physicist's View
  • Probabilistic Interpretation Normalization
  • Consevrvation of Probability Parseval's Theorem
  • Inverse Transform
  • de Broglie Hypothesis Oscillations in Functions
• Fourier Transforms (cont'd)
  • Heisenberg Uncertainty Principle (HUP) Fourier Scale Theorem
  • Momentum Shift Fourier ``Transform space'' Displacement Theorem
  • Position Shift Fourier ``Real Space'' Displacement Theorem
  • Measurement Fourier Convolution Theorem
• Schwartz Inequality
• About this document ...

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