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rtellez700
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Homework Statement
The position-space representation of the radial component of the momentum operator is given by
## p_r \rightarrow \frac{\hbar}{i}\left ( \frac{\partial }{\partial r} + \frac{1}{r}\right ) ##
Show that for its expectation value to be real:## \left \langle \psi|p_r|\psi \right \rangle = \left \langle \psi|p_r|\psi \right \rangle ^{*}##, the radial wave function must satisfy the condition ##u(0)=0##. Suggestion: Express the expectation value in position space in spherical coordinates and integrate by parts.
Homework Equations
##u(r)=r*R(r)##
The Attempt at a Solution
I think this can be solved for a general \psi but I'm having a hard time figuring out where the integration by parts would even come into play. Any insight on how to approach this problem would be appreciated.