(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a wave function [tex]\psi (x,t) = R(x,t) exp(i S(x,t))[/tex] what is the expectation value of momentum?

2. Relevant equations

[tex] <f(x)> = \int^{\infty}_{-\infty} \psi^* f(x) \psi dx[/tex]

[tex] \hat{p} = -i \hbar \frac{\partial}{\partial x} [/tex]

3. The attempt at a solution

This is for an intro to modern class so I don't really have a formal background with eigenvalues/vectors yet so this is a bit confusing.

Can I just say that [tex] <p> = \int^{\infty}_{-\infty} \psi^{*} \hat{p} \psi dx = \int^{\infty}_{-\infty} \hat{p} \psi^{*} \psi dx[/tex] ?

If so by the normalization condition <p> = -i hbar which I don't think can be the case.

So...

[tex]<p> = \int^{\infty}_{-\infty} R exp(-i S) \hat{p} R exp(i S) dx[/tex]

[tex]= -i\hbar \int^{\infty}_{-\infty} R exp(-i S) * [R' exp(i S) + i R S' exp(i S)]dx [/tex]

[tex]= -i\hbar \int^{\infty}_{-\infty} R R' + i R^2 S' dx [/tex]

= ???

I don't really see anything from there...

I'm tempted to just say 0, but I'm not sure that the function being evaluated is odd.

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# Expectation Value of Momentum

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