Phy5646/soham1

(Introduction to Qusntum Mechanics, Griffiths, 2e)Problem 7.14

If the photon has a nonzero mass $(m_{\gamma }\neq 0)$, the Coulomb potential would be rep[laced by the Yukawa potential, $V(r)={\frac {e^{2}}{4\pi \epsilon _{0}}}{\frac {e^{-\mu r}}{r}}$ where $\mu =m_{\gamma }c\hbar$. With a trial wave function of your own devising, estimate the binding energy of a "hydrogen" atom with this potential. Assume $\mu a\ll 1$, and give your answer correct to order $(\mu a)^{2}$