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$\frac{i \hbar}{2m} \int_\text{region} \left((\nabla^2\phi^*) \phi - \phi^* (\nabla^2 \phi) \, \,\right)\mathrm{d}x$

How would I be able to solve this integral using integration by parts or other methods?

($\phi$ is a wave function and $\phi^*$ is used as conventionally.)

This question can be divided into two:

1) When region is $\mathbb{R}^n$

2) When region is some finite shape

3) Should this equation be corrected to $\frac{i \hbar}{2m} \int_\text{region} \left((\nabla^2\phi^*) \phi - \phi^* (\nabla^2 \phi) \, \,\right)\mathrm{d}x \ \mathrm{d}y \ \mathrm{d}z$?

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    This has nothing to do with [tag:contour-integration].2012-10-04

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