# 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

• Degeneracy (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.
• 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.

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