Schrödinger equation in mathematics

Question

I was wondering if it is possible to find mathematics to solve the Schrödinger equation [(-h ^ 2 / 2m) (d ^ 2ψ / dx ^ 2) + kx ^ 2ψ = Eψ] for a particle centered in Origin. When I try to introduce and evaluate the equation, I keep getting the Plus Protected tag.

Answer 1

If you type

eqn = (-h^2/2 m) D[\[Psi][x], {x, 2}] + kx^2 \[Psi][x] == e \[Psi][x] DSolve[eqn, \[Psi][x], x] 

Math will be back

 \[Psi](x)->Subscript[c, 1] Subscript[D, (Sqrt[2] eh Sqrt[k] Sqrt[m])/(2 h Sqrt[k] Sqrt[m])] ((2^(3/4) Power[k, (4)^-1] x)/(Sqrt[h] Power[m, (4)^-1]))+Subscript[c, 2] Subscript[D, (-Sqrt[2] eh Sqrt[k] Sqrt[m])/(2 h Sqrt[k] Sqrt[m])]((I 2^(3/4) Power[k, (4)^-1] x)/(Sqrt[h] Power[m, (4)^-1])) 

which is a solution, given that D stands for ParabolicCylinderD and the subscript [c, 1] and subscript [c, 2] are integration constants.