Weyl-ordered polynomials in fractional-dimensional quantum mechanics

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dc.contributor.authorLohe, M.
dc.contributor.authorThilagam, A.
dc.date.issued2005
dc.descriptionCopyright © 2005 IOP Publishing
dc.description.abstractWe develop algebraic properties of Weyl-ordered polynomials in the momentum and position operators P, Q which satisfy the R-deformed Heisenberg algebra, representations of which describe quantum mechanics in fractional dimensions. By viewing Weyl-ordered polynomials as tensor operators with respect to the Lie algebra sl₂(C) we derive a specific form for these polynomials, including an expression in terms of hypergeometric functions, and determine various algebraic properties such as recurrence relations, symmetries, and also a general product formula from which all commutators and anti-commutators may be calculated. We briefly discuss several applications to quantum mechanics in fractional dimensions.
dc.description.statementofresponsibilityM A Lohe and A Thilagam
dc.identifier.citationJournal of Physics A: Mathematical and Theoretical, 2005; 38(2):461-483
dc.identifier.doi10.1088/0305-4470/38/2/012
dc.identifier.issn1751-8113
dc.identifier.issn0305-4470
dc.identifier.orcidLohe, M. [0000-0002-5214-2225]
dc.identifier.urihttp://hdl.handle.net/2440/17868
dc.language.isoen
dc.publisherIOP Publishing Ltd
dc.source.urihttp://www.iop.org/EJ/abstract/0305-4470/38/2/012/
dc.titleWeyl-ordered polynomials in fractional-dimensional quantum mechanics
dc.typeJournal article
pubs.publication-statusPublished

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