The Schrödinger equation with a simple harmonic potential energy is given by

(1)

where is h-bar, m is the mass of the oscillator, is its angular velocity, and E is its energy. The equation can be made dimensionless by letting

			(2)
			(3)

(4)

becomes

(5)

Now define

			(6)
			(7)

(8)

Quantum Mechanics, Simple Harmonic Oscillator