Weyl-ordered polynomials in fractional-dimensional quantum mechanics
Date
2005
Authors
Lohe, M.
Thilagam, A.
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Journal article
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Journal of Physics A: Mathematical and Theoretical, 2005; 38(2):461-483
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M A Lohe and A Thilagam
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Abstract
We 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.
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Copyright © 2005 IOP Publishing