I learned from the class about the equation for hydrogen atom's electron where textbook assumed that the center/nuclei of hydrogen atom was fixed at origin.
However, since every particle was a wave, the nuclei of the hydrogen atom (say only contain one proton) could be seen a wave as well.
My question was that:
What's the wave equation for the proton in hydrogen atom? Was it simply a traveling wave when the atom was moving, and a Dirac Delta function when it was "fixed"? (Further, what if there was a neutron?)
In the case when hydrogen was traveling, say along $x$ axis, would there be an extra influence/interaction towards the electron's wave equation?
Answer
By conservation of momentum, the center of mass of the atom is what actually stays fixed. This implies that there is a perfect correlation between the wavefunctions $\Psi$ of the electron and $\Phi$ of the proton:
$$\Phi(x)=\Psi(-(M/m)x),$$
where $M$ is the mass of the proton and $m$ is the mass of the electron.
The effect on the energy levels is to replace the electron's mass with the reduced mass.
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