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How do I solve this integral (expectation value) : $\int_{-\infty}^{\infty} \psi (x)^* \hat p \psi (x)\,\text{d}x.$ where the $\hat p =-i\hbar \frac {\partial}{\partial x}$ is an operator and $\psi (x)$ is the wave function.

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    You can't solve this and can't evaluate this integral unless wave function is not specified. In fact you are asking a regular method of evaluation average pulse for all possible wave functions, i.e. for all possible quantum systems!2012-06-14

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