Constrained quantum systems

doi:10.1088/0305-4470/37/21/007

Semiclassical analysis of constrained quantum systems

G F Dell'Antonio et al 2004 J. Phys. A: Math. Gen. 37 5605-5624 doi: 10.1088/0305-4470/37/21/007

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G F Dell'Antonio¹ and L Tenuta²
¹ Department of Mathematics, University of Rome I 'La Sapienza', Piazzale Aldo Moro 2, 00185, Roma, Italy
² Sissa/Isas—International School for Advanced Studies, Via Beirut 2–4, 34014, Trieste, Italy
E-mail: gianfa@sissa.it and tenuta@sissa.it

Abstract. We study the dynamics of a quantum particle in $\field{R}{n+m}$ constrained by a strong potential force to stay within a distance of order planck (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit the evolution of the wavefunction is approximated in norm, up to terms of order planck ^1/2, by the evolution of a semiclassical wave packet centred on the trajectory of the corresponding classical constrained system.

PACS numbers: 03.65.Sq, 03.70.+k, 05.45.Mt

Print publication: Issue 21 (28 May 2004)
Received 11 December 2003, in final form 5 April 2004
Published 12 May 2004

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Semiclassical analysis of constrained quantum systems

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