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Quantum mechanical operator Touchard polynomials studied by virtue of operators' normal ordering and Weyl ordering.
- Source :
-
Modern Physics Letters A . 6/28/2024, Vol. 39 Issue 19/20, p1-7. 7p. - Publication Year :
- 2024
-
Abstract
- In this paper, we propose quantum mechanical operator formalism for Touchard polynomials whose generating function is T n (x) = ∂ n ∂ λ n e (e λ − 1) x | λ = 0. That is replacing e λ x by e λ a † a , where a † a is the number operator, and using the method of integration within ordered product we find that (a † a) n is just the normal ordering form : T n (a † a) :. Then by virtue of the Weyl ordering form of quantum mechanical operator, we also introduce a new special polynomial whose generating function is G n (x) = ∂ n ∂ λ n 2 e λ + 1 exp [ 2 x e λ − 1 e λ + 1 ] | λ = 0. With use of the Weyl ordering form of e λ a † a , we prove (a † a) n = : T n (a † a) : = : : G n (a † a) : : , where : : : : denotes Weyl ordering. It seems that quantum mechancal operator formalism presents a new and simpler approach for generalizing Touchard polynomial theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02177323
- Volume :
- 39
- Issue :
- 19/20
- Database :
- Academic Search Index
- Journal :
- Modern Physics Letters A
- Publication Type :
- Academic Journal
- Accession number :
- 178652448
- Full Text :
- https://doi.org/10.1142/S0217732324500901