Table of Contents

Math Bits - Particle in a 2D Box

Prerequisites

Students should be able to:

  • Write down the energy eigenfunctions and eigenvalues for a 1D infinite square well.
  • Use Fourier series to decompose an arbitrary function into sines (and cosines).
  • Construct the full time-dependent wave function given an initial wave function.

In-class Content

  • Solving the Schrodinger Equation in 2 Dimensions (Lecture, 25 minutes)
  • FIXMEDegeneracy (SGA - 25 min)
    • Each group starts with a different relation between $a$ and $b$, then find:
      1. The energy of the ground state and the corresponding state/ket.
      2. The full wave function (including time dependence) of the ground state.
      3. The energy of at least five excited states and the corresponding state/ket.
        • And their degeneracy if there is more than one state that goes with each energy.
  • FIXMETwo-dimensional Box (SGA - 40 min)
    • For $a=b$, each group gets a different state/ket:
      1. Write the full wave function (including time dependence) of your state.
      2. Plot $\Psi(x,y,0)$ and $\vert\Psi(x,y,0)\vert^2$. Animate them as time progresses.
    • After everyone reports out, if time, everyone should repeat for a superposition.
  • Sturm-Liouville Theory (Lec - 15 min)

Homework for Central Forces

Placeholder question: Particle on a finite cylinder.


Go Back to the Central Forces Course Content Page


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