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I sat down to calculate the expectation value of momentum in the H-atom today, because some kid on another forum wanted to know how fast an electron in an atom is. I was going to calculate [itex]<p>[/itex] and divide it by [itex]m[/itex] for him.

So I wrote down [itex]<p>=\int_V\psi_{100}^*(-i\hbar\nabla)\psi_{100} d^3x[/itex] ([itex]\psi_{100}[/itex] being the ground state H-atom wavefunction). Upon noticing that I've got a solitary [itex]i[/itex] sandwiched between two purely real functions, I didn't even bother to continue. It's going to come out imaginary.

What am I doing wrong?