Massachusetts Institute of Technology

Department of Physics

Physics 8.04 April 25, 1997

Quantum Physics I, Spring 1997

Problem Set 8

(Due Friday, April 25 at 5:00 pm sharp.)

Agenda and required readings for the weeks of April 21:

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.

• --, 04/22: Patriot's Day
• L17, 04/24: Prove relationship between quantum amplitudes and scattered packet sizes, discussion of barrier penetration and reflection at a step, quantum tunneling through a finite barrier and the limit of a barrier, general boundary conditions for a potential.
  Readings: G pp. 74-82

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

• Contents
• List of Figures
• Quiz II, The return: The Quantum Physics of Force at a Reflecting Step
  • Force on the step computed from average number of particles at the step
    • Probability of being on the step
    • Force on the step
  • Force on step computed as momentum change in the incoming particles
    • Probability of Reflection
    • Incoming beam
    • Changes in beam momentum
  • (*) Force on the step from the pressure
• Resonant Transmission: as Seen in Solver Scenario 8
  • Quantum Amplitudes
  • Probabilities for Transmission and Reflection
  • Time delays in resonant transmission
• Tunneling through a function potential: as Seen in Solver Scenario 5
  • Scattering Amplitudes for a potential
  • Scattering Probabilities
  • Time delay
• Resonant Tunneling through two functions: as Seen in Solver Scenario 6
  • Scattering Amplitudes for the double potential
  • Resonant transmission probability
  • Time delay at resonance
• About this document ...

Postscript Version