1. The problem statement, all variables and given/known data 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 2. Relevant equations V(x) = (1/2)kx^2 time independant equation: 3. 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 im not sure where to go from here. does anybody know what to do or a website that tells how to do this proof?