The analytical solution for the wavefunction of a hydrogenic electron with quantum numbers n, l and m has a spherical harmonic part that involves theta and phi (in spherical coordinates). I was looking in Griffiths, and the spherical harmonics part only has phi as exp(i m phi) where i is the imaginary unit, m is the magnetic quantum number and phi is phi (sorry I didn't use TeX). Phi doesn't show up in any other way, than attached to an i in an exponential...(adsbygoogle = window.adsbygoogle || []).push({});

So the complex conjugate of the wave function multiplied by the wave function itself should kill all the terms with phi. Am I correct?

How does phi factor into the probability density? Isn't it removed in taking psi*psi? I am trying to sketch the probability densities of hydrogen's first few wavefunctions.

Thank you for any help.

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# Where does phi go in the probability density for hydrogen?

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