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Gauge transformations for a driven quantum particle in an infinite square well

Weigert, S. (1999) Gauge transformations for a driven quantum particle in an infinite square well. Foundations of Physics. pp. 1785-1805. ISSN 0015-9018

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Abstract

Quantum mechanics of a particle in an infinite square well under the influence of a time-dependent electric field is reconsidered. In some gauge, the Hamiltonian depends linearly on the momentum operator which is symmetric but not self-adjoint when defined on a finite interval. In spite of this symmetric part, the Hamiltonian operator is shown to be self-adjoint. This follows from a theorem by Kato and Rellich which guarantees the stability of a self-adjoint operator under certain symmetric perturbations. The result, which has been assumed tacitly by other authors, is important in order to establish the equivalence of different Hamiltonian operators related to each other by quantum gauge transformations. Implications for the quantization procedure of a particle in a box are pointed out.

Item Type: Article
Copyright, Publisher and Additional Information: © 1999 Plenum Publishing Corporation. This is an author produced version of a paper published in Foundations of Physics.
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 23 Jun 2006
Last Modified: 17 Oct 2013 14:39
Published Version: http://dx.doi.org/10.1023/A:1018878014253
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1374

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