.

For , this reduces to an isotropic two-dimensional oscillator. The Schrödinger equation

can be solved exactly using the variable transformation

,

,

which reduces the Hamiltonian to the separable form

,

where

,

.

The ground state is given by

,

while the first excited state is

.

You can display three-dimensional plots of these states, with selected values of and , or the nonstationary state

.

Varying the time shows the oscillation of this coupled two-dimensional oscillator. This is the main feature of this Demonstration.