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Apr 25, 2023 at 18:18 comment added J. Murray @Zorbakk I mean, you could simply observe that the integrand doesn't have any angles in it. It depends only on $r$.
Apr 25, 2023 at 9:27 comment added Zorbakk I see. Thank you for your very concrete answer. I have one more question though. You said that the wave function is spherically symmetric, is there a way to check this easily or do I just have to calculate the integral when in spherical coordinates?
Apr 24, 2023 at 22:32 comment added J. Murray @Zorbakk Yes - that state is normalizable, and the expected values in question would all be finite (and zero, unsurprisingly, since the wavefunction is spherically symmetric). It is not an eigenstate of the free-particle Hamiltonian (which you can easily check), but that's okay - it only means that the wavefunction will change non-trivially with time.
Apr 24, 2023 at 18:02 comment added Zorbakk Thank you for your answer, you made it very clear for me. I did realize however as other people have pointed out that I did forget to include a minus sign in front of $r\gamma$, would this change the outcome somehow?
Apr 24, 2023 at 18:00 vote accept Zorbakk
Apr 24, 2023 at 16:34 history answered J. Murray CC BY-SA 4.0