q-Quantum Mechanics on T n

Reidun Twarock
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Reidun Twarock: TU Clausthal, Arnold Sommerfeld Institut

A chapter in Symmetries in Science X, 1998, pp 435-441 from Springer

Abstract: Abstract In [1] and [2] a version of a q-quantum mechanics on S 1 has been presented, which is given entirely in terms of discrete derivatives and is thus suitable for an application to physical systems which are defined over a discrete configuration space S 1 N consisting of the N-th roots of unity. The motivation for this version was explained in [3]. Here, an extension of the formalism of this version to the n-dimensional torus T n ≅S 1×... × S 1is discussed. It is shown that the results for T n can be derived canonically from those fo S 1. It is the first step in the generalization of q-Borel quantization and the corresponding q-quantum mechanics to higher dimensional manifolds. As in the case of S 1, one obtains in the limit q→ 1 additional information on the dynamics in the undeformed situation.

Keywords: Shift Operator; Schrodinger Equation; Nonlinear Schrodinger Equation; Discrete Derivative; Witt Algebra (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-1537-5_28

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DOI: 10.1007/978-1-4899-1537-5_28

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