Principles of Quantum Mechanics · Problem 13.1.4

The Hydrogen Atom — R. Shankar

Physics — Quantum Mechanics · hydrogen-asymptotic-behavior

Problem

Recall from the last chapter [Eq. (12.6.19)] that as r→∞r \to \infty, UE∼(r)me2/κℏ2e−κrU_E \sim (r)^{me^2/\kappa\hbar^2} e^{-\kappa r} in a Coulomb potential V=−e2/rV = -e^2/r [κ=(2mW/ℏ2)1/2][\kappa = (2mW/\hbar^2)^{1/2}]. Show that this agrees with Eq. (13.1.26).

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