Bridge B
Solutions to the Schrödinger Equation

Cf Krane, Chapts 5 & 7, or any standard Modern Physics text

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Wave Equations

  • Expectation value equations
  • Separation of variables

    • Particle in a Box

  • Constant potential, named series
  • Expansion solution
  • (continued)
  • Infinite square well
  • Boundary conditions
  • Normalization
  • Solutions
  • Finite square well
  • Solutions

    • Barrier penetration

  • Barrier penetration
  • Tunnelling
  • Simultaneous solution
  • Reflections and transmission
  • WKB approximation
  • Examples of tunnelling
  • Ammonia maser
  • STM animation

    • Harmonic Oscillator

  • Natural units; radial diff. equ.
  • Ansatz for 2-term recursion
  • Recursion relation
  • Termination condition
  • Wave function plots
  • Probability plots
  • Plot n=10
  • Hermite polynomials

    • Three Dimensional Problems

  • Separation of variables
  • Solutions for 4 equations
  • Quantization and operators
  • Legendre equation
  • Legendre polynomials
  • Associated Legendre polynomials
  • Spherical harmonics
  • Uncertainty relations

    • Coulomb Potential

  • Natural units
  • Ansatz for 2-term recursion
  • Laguerre solution
  • Laguerre polynomials
  • Connection to isotropic SHO   [Current Position]
  • Numerical solution
  • Curtis & Ellis, Am. J. Phys. 72, 1521 (2004).
  • Curtis & Ellis, Eur. J. Phys. 27, 485 (2006)
  • Larkoski, Ellis & Curtis, Am. J. Phys. 74, 572 (2006)
  • French mathematicians


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    Chapter 2
    Bridge A
    Chapter 3
    Chapter 4
    Chapter 5

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