Principles of Quantum Mechanics · Problem 12.6.1

Rotational Invariance and Angular Momentum — R. Shankar

Physics — Quantum Mechanics · radial-equation-rotationally-invariant

Problem

A particle is described by the wave function ψE(r,θ,ϕ)=A e−r/a0(a0=const)\psi_E(r,\theta,\phi) = A\, e^{-r/a_0} \qquad (a_0 = \text{const}) (1) What is the angular momentum content of the state? (2) Assuming ψE\psi_E is an eigenstate in a potential that vanishes as r→∞r \to \infty, find EE. (Use leading terms in Schr\"odinger's equation.) (3) Having found EE, consider finite rr and find V(r)V(r).

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