Introduction to Quantum Mechanics · Problem 8.21

The Variational Principle — David J. Griffiths

Physics — Quantum Mechanics · variational_yukawa_potential

Problem

If the photon had a nonzero mass (mγ≠0)(m_\gamma \neq 0), the Coulomb potential would be replaced by the Yukawa potential, V(r)=−e24πϵ0e−μrr,(8.73)V(r) = -\frac{e^2}{4\pi\epsilon_0}\frac{e^{-\mu r}}{r}, \qquad (8.73) where μ=mγc/ℏ\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 μa≪1\mu a \ll 1, and give your answer correct to order (μa)2(\mu a)^2.

Related theory

Browse the problem library