Year: 2025
Type: article
Abstract: This study derives the normal ordering expansion of degenerate integral powers of the number operator, (a†a)_{n,λ}, using recurrence relations for the coefficients and an operator action on number states. Here a† and a are respectively the boson creation and annihilation operators. We also determine the inverse of this normal ordering expansion. By analyzing diagonal coherent state elements of the degenerate integral powers of the number operator, we establish a combinatorial identity which yields a Dobinski-like formula for the degenerate Bell numbers at a specific value, connecting degenerate quantum operator calculus with combinatorics.
Authors: Taekyun Kim, Dae San Kim, Kyo-Shin Hwang
Institutions: Kwangwoon University, Yeungnam University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415935607
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