Normal ordering of degenerate integral powers of number operator and its applications
Taekyun Kim, Dae San Kim, Hye Kyung Kim
Abstract
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 degenerate integral power of the number operator in terms of boson operators, which is represented by means of the degenerate Stirling numbers of the second kind. As an application of this normal ordering, we derive two equations defining the degenerate Stirling numbers of the second kind and a Dobinski-like formula for the degenerate Bell polynomials.
Topics & Concepts
Degenerate energy levelsOperator (biology)Stirling numberStirling numbers of the first kindBell polynomialsMathematicsStirling numbers of the second kindBosonStirling engineCreation and annihilation operatorsPure mathematicsAlgebra over a fieldQuantum mechanicsPhysicsQuantumGeneTranscription factorChemistryRepressorBiochemistryThermodynamicsAdvanced Mathematical IdentitiesMathematical functions and polynomialsMathematical Inequalities and Applications