Massachusetts Institute of Technology

Department of Physics

Physics 8.04 February 20, 1997

Quantum Physics I, Spring 1997

Problem Set 3

(Due Friday, February 28 at 5:00 pm sharp.)

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

• L6, 02/25: HUP and energy: electron in a box, classical limit, H-atom, discrete spectra.
  G 33-38; CN ``Heisenberg Uncertainty Principle''
• L7 02/27: BS Quantization applied to H-atom, classical limit, , Franck-Hertz expt.
  RH 4.7, 7.4-7.7; G 15-21; CN ``Bohr-Sommerfeld Quantization and the Classical Limit''

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 .

• List of Figures
• Contents
• Spreading of the Gaussian Wave Packet (25 pts)
• Quantum Pinball (25 pts)
  • Analysis of a single collision
  • Uncertainty in ball's direction after the first collision
  • Magnification of errors
  • Perfect gambling device
• Order of Magnitude Estimates from the HUP (25 pts)
  • Potential Energy
  • Kinetic Energy
  • Minimum Total Energy and Contributions
  • Energy of Confinement
  • Balance between Kinetic and Potential Energy
  • Correspondence Principle
  • Make Your own Estimate of the Energy and Size of the Hydrogen Atom
• Semiquantitative Results Using Semiclassical Quantization/Correspondence Principle and Energy Spacing (25 pts)
  • Classical orbits
  • Semiclassical quantization
  • Comparison with Results from the HUP
  • Correspondence Principle Argument
  • Spacing Between States
  • Example of Exploiting the Correspondence Principle
  • Your own Calculation of the Energy of the Hydrogen Atom
• About this document ...

Postscript Version