Schrodinger's Equation in Mathematica

Question

I was wondering if there was any way to have mathematica find the solution to Schrodinger's equation [(−h^2/2m)(d^2ψ/dx^2) + kx^2ψ=Eψ] for a particle centered at the origin. I keep getting a Tag Plus Protected error when I try to enter and evaluate the equation.

Answer 1

If you type

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

 DSolve[eqn, \[Psi][x], x]

Mathematica will return

\[Psi](x)->Subscript[c, 1] Subscript[D, (Sqrt[2] e-h 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] e-h 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 the solution keeping in mind that D stands for ParabolicCylinderD and Subscript[c, 1] and Subscript[c, 2] are constant of integration.