- #1
torq123
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Homework Statement
What is the average momentum for a packet corresponding to this normalizable wavefunction?
[itex]\Psi(x) = C \phi(x) exp(ikx) [/itex]
C is a normalization constant and [itex]\phi(x) [/itex] is a real function.
Homework Equations
[itex]\hat{p}\rightarrow -i\hbar\frac{d}{dx}[/itex]
The Attempt at a Solution
[itex]\int\Psi(x)^{*}\Psi(x)dx = \int C^2 \phi(x)^{2}dx= 1 [/itex]
Plugging in the momentum operator and using the chain rule:
[itex]<\hat{p}> = \hbar k \int C^2 \phi(x)^2 dx - i \hbar \int C^2 \phi^{'}\phi dx [/itex]
The second term is always imaginary since [itex]\phi(x)[/itex] is real, so I said the momentum is [itex]\hbar k[/itex] which I think might be right, but for the wrong reasons? I didn't think Hermetian operators could give imaginary expectation values...