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**techmath** Show that a solution for S.E. for a free particle in three dimensions can be written as:

*ħ^2/2m(d^2/dx^2 + **d^2/dy^2 + **d^2/dz^2**)*Ψ(x,y,z) = EΨ(x,y,z)

Ψ(x,y,z)= A*exp(iK*r)

How is K related to E?

How does the corresponding timedependent function look like?

(Hint: Suppose Ψ(x,y,z)=Ψ(x)*Ψ(y)*Ψ(z) and separate the function )

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I just derivated Ψ(x,y,z) two times and inserted it into the equation, but i dont think its enough....