We solve the boson normal ordering problem for (q(a†)a + v(a†))nwith 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 eλ(q(a†)a + v(a†))generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures. © 2006 IOP Publishing Ltd.
|Publication status||Published - 28 Feb 2006|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Penson, K. A., Blasiak, P., Dattoli, G., Duchamp, G. H. E., Horzela, A., & Solomon, A. I. (2006). Monomiality principle, Sheffer-type polynomials and the normal ordering problem. https://doi.org/10.1088/1742-6596/30/1/012