Aharonov-Bohm shift as a shift in normal coordinates

Abstract

The Aharonov-Bohm shift in a closed system is considered. The solenoid is a charged, rotating cylinder which is electrically neutral. This model of Henneberger and Opatrny has a Hamiltonian which is a quadratic form. This quadratic form is transformed to normal coordinates, so that the stationary states become self-evident. It is shown that, in the original system, it is the kinetic angular momentum which is quantized. Solutions of the problem for an electron inside the solenoid are discussed. It is shown that the rotating cylinder exhibits different behavior if the electron is in the magnetic field or if it is in the external region. An external field approximation which replaces the cylinder by a constant magnetic field therefore cannot yield a correct solution of the Schrödinger equation which is continuous at the surface of the solenoid.