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I was using this to derive the TDSE. But I ran into problem because to substitute k^2 in E=h^2/8mpi^2 * k^2, I can use single derivative of psi squared or double derivative, both of which tend to give the correct answer. So, is my assumption of energy wrong?

PS

I am using psi = e^i(kx-wt) as my wave function. Single derivative squared or double derivative both have k^2.

Substituting this gives two different equations.