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IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 43 (2010) 474002 (14pp) doi:10.1088/1751-8113/43/47/474002
 

Summary: IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL
J. Phys. A: Math. Theor. 43 (2010) 474002 (14pp) doi:10.1088/1751-8113/43/47/474002
A constant of quantum motion in two dimensions in
crossed magnetic and electric fields*
Joachim Asch1
and C´edric Meresse2
1 CPT-CNRS UMR 6207, Universit´e du Sud, ToulonVar, BP 20132,F­83957 La Garde Cedex,
France
2 CPT-CNRS UMR 6207, CNRS Luminy, Case 907 13288 Marseille Cedex 9, France
E-mail: asch@cpt.univ-mrs.fr and meresse@cpt.univ-mrs.fr
Received 30 May 2010, in final form 16 September 2010
Published 9 November 2010
Online at stacks.iop.org/JPhysA/43/474002
Abstract
We consider the quantum dynamics of a single particle in the plane under the
influence of a constant perpendicular magnetic and a crossed electric potential
field. For a class of smooth and small potentials we construct a non-trivial
invariant of motion. To do so we prove that the Hamiltonian is unitarily
equivalent to an effective Hamiltonian which commutes with the observable of
kinetic energy.

  

Source: Asch, Joachim - Centre De Physique Theorique, Campus de Luminy, Case 907

 

Collections: Mathematics