Representations of monomiality principle with Sheffer-type polynomials and boson normal ordering
نویسندگان
چکیده
منابع مشابه
Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering
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...
متن کاملMonomiality principle, Sheffer-type polynomials and the normal ordering problem
We solve the boson normal ordering problem for ( q(a†)a+ v(a†) )n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] = 1. This consequently provides the solution for the exponential e †)a+v(a†)) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle...
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We solve the boson normal ordering problem for (q(a)a + v(a)) with arbitrary functions q and v and integer n, where a and a are boson annihilation and creation operators, satisfying [a, a] = 1. This leads to exponential operators generalizing the shift operator and we show that their action can be expressed in terms of substitutions. Our solution is naturally related through the coherent state ...
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The Sheffer polynomials and the monomiality principle, along with the underlying operational formalism, offer a powerful tool for investigation of the properties of a wide class of polynomials. We present, within such a context, a self-contained theory of such familiar systems of polynomials as the Euler, Bernoulli, Bessel and other clasical polynomials and show how the derivation of some of th...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 2006
ISSN: 0375-9601
DOI: 10.1016/j.physleta.2005.11.052