From sequences to polynomials and back, via operator orderings

Journal Article · Sun Dec 15 00:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4836778· OSTI ID:22251756

Amdeberhan, Tewodros; Dixit, Atul; Vignat, Christophe ^[1]

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1. Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA and L.S.S. Supelec, Universite d'Orsay (France)

Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

• OSTI ID: 22251756
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL OPERATORS
POLYNOMIALS
YIELDS