The simple harmonic oscillator models the motion of a wavefunction subject to the potential function
illustrated below.
The Schrodinger equation becomes
The first few solutions, in order of increasing energy, are shown below. In this table
and 
|
Quantum Number |
Energy Eigenvalue |
Wavefunction |
|
0 |
|
|
|
1 |
|
|
|
2 |
|
|
|
3 |
|
|
|
4 |
|
|
These wavefunctions are illustrated below. The minimum possible energy is
.
