Chapter 1 - The Wave Function
Semiclassical Conceptual Models

Probabilities

  • Discrete outcomes
  • Coin tosses
  • Quantum coins
  • Coin distribution function
  • Dice casting
  • Quantum dice
  • Shared birthdays
  • approximated
  • Stirling's approximation
  • N objects taken n at a time
  • Related to binomial distribution
  • Problem 1.13 - Buffon's needle

    • Continuous Probabilities

  • Integration
  • Dice casting
  • continued

    • Probabilistic formulation of dynamics

  • Dwell time
  • Momentum formulation

    • Least action principle

  • Least time
  • Fermat's principle applet
  • Least action
  • Least action applet
  • A call to action, Am.J.Phys. 71, 423 (2003)
  • Feynman and least action

  • Exercise
  • Solution
  • Plot

    Quantized action

  • EBK quantization
  • Examples: Circular orbit and box
  • BSW
  • Example: SHO

    Summary

  • Defining equations

    Dwell time of falling objects

  • Formulation
  • Average values
  • Dwell time within one sigma
  • Perturbation with altitude
  • Numerical solution

    • Molecule in a room

  • Microscopic origin of pressure
  • van der Waals equation
  • Probability formulation
  • Box quantization
  • Energy levels
  • Classical and BSW
  • Mean position
  • Mean square position
  • Measurements
  • Variance and standard deviation
  • Variance of distributions
  • Experimental testing

    • Harmonic oscillator

  • Classical dwell time
  • Average values
  • Analytic solution
  • Numerical solution
  • Action quantization
  • Numerical solution
  • Newton-Raphson method
  • Distributions
  • Anharmonic well
  • Perturbation expansion
  • Accepted QM solution

    Semiclassical Quantization

  • EKB Quantization
  • EKB References
  • Sommerfeld and Caustics
  • Caustic animation
  • In original language
  • A.Einstein, Deutsche Physikalische Gesellschaft 19 (1917).
  • Stone essay
  • J.B. Keller, Ann. Phys. (NY) 4, 180 (1958).

    Exercise

  • Morse Potential dwell time Exercise
  • Solution
  • Morse Potential EBK Exercise