Degenerate r-Bell Numbers and Coherent States
Abstract
This paper derives the normal ordering expansion for the operator $$(a^{\dagger}a+r)_{n,\lambda}$$ , using two methods: the action of the generalized displacement operator on number states and the determination of a recurrence relation for expansion coefficients. Here $$a^{\dagger}$$ and $$a$$ are respectively the boson creation and annihilation operators. We also deduce the inverse relation for this expansion. Applying coherent state techniques, we establish identities for the diagonal matrix elements $$\langle z| (a^{\dagger} a+r)_{k,\lambda}|z\rangle$$ , which directly yield a Dobinski-like formula for the degenerate $$r$$ -Bell numbers. Furthermore, we present a new recurrence relation for these combinatorial numbers.
Fields of Study & Subjects
Quantum Mechanics and Non-Hermitian Physics
Advanced Mathematical Identities
Mathematical functions and polynomials
Publication details
- Journal / source
- Russian Journal of Mathematical Physics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 33
- Issue
- 2
- Pages
- 332–339
- Publication date
- 1 June 2026
- Language
- EN