# Quantum Mechanics Photons

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The photon is normally assumed to have zero rest mass. If the photon had a small mass, this would alter the potential energy which the electron experiences in the electric field of the proton. Instead of

V(r) = -(e^2)/(4(pi)(epsion_0)(r))

we would have

V(r) = -((e^(2))(e^(-r/r_0)))/(4(pi)(epsilon_0)(r))

where r_0 is a constant with units of length. Assume r_0 is large compared to the size of the hydrogen atom, so the potential energy given in the second equation above differs only slightly from the standard one given by the first equation in the vicinity of the electron. Calculate the change in the ground state energy of hydrogen if the correct potential is given by the second equation instead of the first one.

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The original unperturbed Hamiltonian is:

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