Solution to the Schrodinger equation

cytochrome
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I know that one solution to the Schrodinger equation is

Aexp(i(kx - ωt))

Is there a special relationship between k and ω for this to be a solution, or is it always a solution?
 
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That's the solution for a free particle. You can work out the dispersion relationship easily.

The energy is only kinetic, p = hk (that should be h bar), E = hω (again, h bar).
 

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