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Series in optics and optoelectronics

The scalar potential and electromagnetic interaction Hamiltonian

Published Oct 30, 2004• 0 citations
Publisher
DOI
10.1201/9781420056990.axv

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Abstract In this article, we review a new approach to the scalar Aharonov-Bohm effect for both the electromagnetic and gravitational interaction. For both interactions a quantum system is placed in a time-dependent electromagnetic or gravitational potential, but with no force (spatial derivative of the potential) acting on the quantum system. Nevertheless, we show that the energy levels of the quantum system develop side bands which can be detected as the signature of this version of the scalar Aharonov-Bohm effect. We briefly look at the specific experimental setups required to detect the energy side bands.
When the electromagnetic field is adiabatically switched on and subsequently switched off, the vector and scalar potentials can still be nonzero when the electromagnetic fiele is zero. In this case it is necessary to use the energy operator, not the Hamiltonian, to calculate the probability that the system is in an energy eigenstate. In the gauge in which the potentials are zero when the field is zero, the energy operator reduces to the unperturbed Hamiltonian and the usual procedure for calculating probabilities can be used.