Schrodinger Eqn: Simple Harmonic Oscillator

[Oerg]

Hi,

is this the time independent Schrödinger equation for a simple harmonic oscillator?

$$-\frac{1}{2}\frac{d^{2}\psi}{dx^2}+\frac{1}{2}x^{2}\psi(x)=\epsilon\psi(x)$$

where epsilon is the rescaled energy eigenvalue.

 

[maverick280857]

Hi,

is this the time independent Schrödinger equation for a simple harmonic oscillator?

$$-\frac{1}{2}\frac{d^{2}\psi}{dx^2}+\frac{1}{2}x^{2}\psi(x)=\epsilon\psi(x)$$

where epsilon is the rescaled energy eigenvalue.

Yup, in one dimension.

 

[Oerg]

is it really? because i tried to find out the eigenvalues by integrating with euler's method and i can't find any values for epsilon such that the boundary condition $$\psi(\infty)=0$$ is satisfied.

 

[kuruman]

Maybe your method is flawed. You know what the energy for a harmonic oscillator is. Have you tried to put in that value, say for the ground state, and see whether the boundary condition is satisfied?