Quantum Mechanical Inclusion of the Source in the Aharonov-Bohm Effects

Abstract

Following semiclassical arguments by Vaidman we show, for the first time in a fully quantum mechanical way, that the phase shifts arising in the Aharonov Bohm (A-B) magnetic or electric effects can be treated as due to the electric force of a classical electron, respectively acting on quantized solenoid particles or quantized capacitor plates. This is in contrast to the usual approach which treats both effects as arising from non-field producing potentials acting on the quantized electron. Moreover, we consider the problems of interacting quantized electron and quantized solenoid or quantized capacitor to see what phase shift their joint wave function acquires. We show, in both cases, that the net phase shift is indeed the A-B shift (for, one might have expected twice the A-B shift, given the above two mechanisms for each effect.) The solution to the exact Schrodinger equation may be treated (approximately for the magnetic A-B effect, which we show using a variational approach, exactly for the electric A-B effect) as the product of two solutions of separate Schrodinger equations for each of the two quantized entities, but with an extra phase. The extra phase provides the negative of the A-B shift, while the two separate Schrodinger equations without the extra phase each provide the A-B phase shift, so that the product wave function produces the net A-B phase shift.

This paper includes all that was correct in the previous version. However, unlike that version, the present paper shows that the Aharonov-Bohm phase shift is obtained when the electron and solenoid are both quantized. A better approximation to the wave function for electron and solenoid than used previously is obtained from the variational principal for the Schrodinger equation

References in corpus (1)

• Quantizing the Vector Potential Reveals Alternative Views of the Magnetic Aharonov-Bohm Phase Shift

Cited by in corpus (14)

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• Quantizing the Vector Potential Reveals Alternative Views of the Magnetic Aharonov-Bohm Phase Shift
• Local description of the Aharonov-Bohm effect with a quantum electromagnetic field
• Coherence and realism in the Aharonov-Bohm effect
• Aharonov-Casher and shielded Aharonov-Bohm effects with a quantum electromagnetic field
• Gauge independent description of Aharonov-Bohm Effect
• Aharonov-Bohm effect with an effective complex-valued vector potential
• The Aharonov-Bohm effect in a closed flux line
• Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem
• Gauge invariance of the Aharonov-Bohm effect in a quantum electrodynamics framework
• Gauge dependence of the Aharonov-Bohm phase in a quantum electrodynamics framework
• Topology of the Aharonov-Bohm effect in different reference frames
• The classical counterpart of the Aharonov-Bohm phase