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## Homework Statement

Show by direct substitution into the time-independent Schrodinger equation that such a particle could be described by the state function

Ψ(x) = Ψ_0exp(-ax^2) with a, Ψ_0 constants

## Homework Equations

V(x) = (1/2)kx^2

time independant equation:

## The Attempt at a Solution

i found d2Ψ/dx2 = Ψ(4a^2x^2-2a)

then i plugged that and V(x) into the formula and get:

(-h^2/2m)[4a^2x^2 - 2a]Ψ + Ψ(1/2)kx^2 = EΨ

then divided Ψ out and multiplied out the left side and got:

(-2h^2a^2x^2/m) +ah^2/m + (1/2)kx^2 = E

now I am not sure where to go from here. does anybody know what to do or a website that tells how to do this proof?