Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering

Details Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering

2005-04-02

arxiv.org/abs/quant-ph/0504009v1

Phys. Lett. A 352, 7-12 (2006)

Physics

Quantum Physics

9 pages

Scientific paper

We construct explicit representations of the Heisenberg-Weyl algebra [P,M]=1 in terms of ladder operators acting in the space of Sheffer-type polynomials. Thus we establish a link between the monomiality principle and the umbral calculus. We use certain operator identities which allow one to evaluate explicitly special boson matrix elements between the coherent states. This yields a general demonstration of boson normal ordering of operator functions linear in either creation or annihilation operators. We indicate possible applications of these methods in other fields.

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