Scattering of a Charged Particle from a Hard Cylindrical Solenoid: Aharonov-Bohm Effect

Abstract

The scattering amplitude fk (α, θ) of a charged particle from a long hard cylindrical solenoid is derived by solving the time independent Schrodinger equation on a double connected plane. The amplitude is expressed by a summation over the angular momentum quantum number m (partial wave summation). It is shown that only negative mechanical angular momenta, m+α＜0, contribute to the amplitude when the radius of the solenoid goes to the zero limit (a→0) without varying the magnetic induction flux α = Φ_B/Φ_0 (flux line). The original Aharonov-Bohm result is obtained with this limit.