- #1

Yoni V

- 44

- 0

## Homework Statement

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##.

## Homework Equations

## 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