Weigert, S. (1999) Gauge transformations for a driven quantum particle in an infinite square well. Foundations of Physics. pp. 17851805. ISSN 00159018

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Abstract
Quantum mechanics of a particle in an infinite square well under the influence of a timedependent electric field is reconsidered. In some gauge, the Hamiltonian depends linearly on the momentum operator which is symmetric but not selfadjoint when defined on a finite interval. In spite of this symmetric part, the Hamiltonian operator is shown to be selfadjoint. This follows from a theorem by Kato and Rellich which guarantees the stability of a selfadjoint 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. 
Institution:  The University of York 
Academic Units:  The University of York > Mathematics (York) 
Depositing User:  Repository Officer 
Date Deposited:  23 Jun 2006 
Last Modified:  25 Apr 2015 19:43 
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 