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## Homework Statement

Determine whether the wave function [itex]\Psi (x,t)= \textrm{exp}(-i(kx+\omega t))[/itex] is an eigenfunction of the operators for total energy and x component of momentum, and if it is, calculate the eigenvalues.

## Homework Equations

Condition for an eigenfunction:

[tex]\hat{E}\Psi =k\Psi [/tex]

Where K is the eigenvalue

Energy operator:

[tex]\hat{E}=i\hbar\frac{\partial }{\partial t}[/tex]

## The Attempt at a Solution

Determining that psi is an eigenfunction is easy enough.

[tex]\hat{E}\Psi =i\hbar\frac{\partial }{\partial t}[\textrm{exp}(-i(kx+\omega t))][/tex]

[tex]=-i\hbar i\omega \Psi =\hbar\omega \Psi =\frac{h}{2\pi }2\pi f\Psi =hf\Psi =E\Psi [/tex]

I can't figure out how to calculate the value of E from this information alone. I imagine the same method works for momentum when I figure out what it is.