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 .