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