Related papers: Sheffer Polynomials and the s-ordering of Exponent…
We solve the boson normal ordering problem for (q(a*)a + v(a*))^n 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…
Ordering identities in the Weyl-Heisenberg algebra generated by single-mode boson operators are investigated. A boson string composed of creation and annihilation operators can be expanded as a linear combination of other such strings, the…
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.…
By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators (which considers normal ordered, antinormally ordered and Weyl…
We solve the boson normal ordering problem for $(q(a^\dag)a+v(a^\dag))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^\dag$ are boson annihilation and creation operators, satisfying $[a,a^\dag]=1$. This…
We address a systematic combinatorial approach to the anti-normal ordering problem. In this way, we use the Stirling numbers and their generating function, the so-called Bell polynomials, together with the operational methods to anti-normal…
The normal ordering of an integral power of the number operator in terms of boson operators is expressed with the help of the Stirling numbers of the second kind. As a `degenerate version' of this, we consider the normal ordering of a…
In a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have…
We discuss a general combinatorial framework for operator ordering problems by applying it to the normal ordering of the powers and exponential of the boson number operator. The solution of the problem is given in terms of Bell and Stirling…
In this article, the 2-iterated Sheffer polynomials are introduced by means of generating function and operational representation. Using the theory of Riordan arrays and relations between the Sheffer sequences and Riordan arrays, a…
A new integral representation is obtained for the star product corresponding to the $s$-ordering of the creation and annihilation operators. This parametric ordering convention introduced by Cahill and Glauber enables one to vary the type…
Some $q-$analogues of the normal ordering of the operator $(X+sD)^n$ on the polynomials are derived.
In this paper we develop the generalised Schur theory offered in the recent paper by the second author in dimension one case, and apply it to obtain a new explicit parametrisation of torsion free rank one sheaves on projective irreducible…
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear…
In quantum mechanics, bosonic operators are mathematical objects that are used to represent the creation ($a^\dagger$) and annihilation ($a$) of bosonic particles. The natural power of a linear combination of bosonic operators represents an…
Let $\Phi$ be an (LB)-space over $\mathbb F=\mathbb R$ or $\mathbb C$, and let $\Phi'$ be the dual space of~$\Phi$. We study the set $\mathbb S(\Phi)$ of Sheffer operators acting in polynomials on $\Phi'$. We prove that $\mathbb S(\Phi)$ is…
Inspired by the framework of operational methods and based on the generating functions of Legendre-Gould Hopper polynomials and Sheffer sequences, we discuss certain new mixed type polynomials and their important properties. We show that…
The purpose of this article is to give a Chlodowsky type generalization of Szasz operators defined by means of the Sheffer type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order…
The present work deals with the mathematical investigation of some generalizations of the Sz\'{a}sz operators. In this work, the multiple Sheffer polynomials are introduced. The generalization of Sz\'{a}sz operators involving multiple…
We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to…