## The Simple Harmonic Oscillator

The simple harmonic oscillator models the motion of a wavefunction subject to the potential functionillustrated below.

The Schrodinger equation becomes

The first few solutions, in order of increasing energy, are shown below. In this tableand

Quantum Number | Energy Eigenvalue | Wavefunction |

0 | ||

1 | ||

2 | ||

3 | ||

4 |

These wavefunctions are illustrated below. The minimum possible energy is .