# Harmonics Oscillator

1. Apr 25, 2009

### Winzer

1. The problem statement, all variables and given/known data

Show:
$$\psi_1=N x e^{-\frac{x^2}{\sigma}}$$ is an eigenfunction of the total energy operator(H).

2. Relevant equations
psi=N x exp[-x^2/K]

3. The attempt at a solution
I plugged in the above to the Schrodinger Equation-time indep. for Harmonic oscillator but I keep getting an x^2 dependence inside the calculation. Do I not plug this in?

2. Apr 25, 2009

### Winzer

oh, I should be putting psi into d^2(psi)/dy^2 + (e-y^2) psi =0 where y=sqrt(mw/h) x. the asymtotic solution: e-->0. This is what is I should plug it into right?