Is energy contained in matter wave equals hv like EM waves?

[Jaden159]

h is plank constant and v is frequency.
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.

 

[PeterDonis]

I was using this to derive the TDSE.

Starting with what assumptions? Just saying "h is Planck's constant and v is frequency" isn't enough by itself.

 

[king vitamin]

Single derivative squared is not linear, whereas linearity is probably an assumption you want (though as PeterDonis said, you haven't stated what assumptions you want to start with fully).