# Potential in center of mass for Hydrogen atom

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1. Jan 14, 2017

### Yoni V

1. The problem statement, all variables and given/known data
A Hydrogen atom is interacting with an EM plane wave with vector potential
$$\bar A(r,t)=A_0\hat e e^{i(\bar k \cdot \bar r -\omega t)} + c.c.$$
The perurbation to the Hamiltonian can be written considering the proton and electron separately as
$$V(t)=-\sum_{i=1,2}\frac{q_i}{2m}\bar P_i\cdot \bar A(R_i ,t)$$
Write the potential in terms of the center of mass and reduced mass $r,R_c$.

2. Relevant equations

3. The attempt at a solution
This is just part of the exercise, but the one I'm stuck at. I initially thought I only need to substitute
$$m_1\rightarrow \mu ,\; m_2 \rightarrow M,\;P_1\rightarrow p ,\; P_2 \rightarrow P_C$$ etc. but it doesn't seem to fit the results that follow in the rest of the exercise. Also, I don't know what to make of the charges - how are they supposed to be transformed? Thanks

2. Feb 13, 2017

### Staff: Admin

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

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