Calculating Normal-Ordered Forms in Fock Space by Quantum White Noise Derivatives

Un Cig JI; Nobuaki OBATA

doi:10.4036/iis.2013.201

Interdisciplinary Information Sciences

Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050

Calculating Normal-Ordered Forms in Fock Space by Quantum White Noise Derivatives

Un Cig JI, Nobuaki OBATA

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Keywords: Boson Fock space, normal-ordered form, quadratic annihilation and creation operator, quantum white noise, Wick product

JOURNAL FREE ACCESS

2013 Volume 19 Issue 2 Pages 201-211

DOI https://doi.org/10.4036/iis.2013.201

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Abstract

The normal-ordered form of the composition of the exponential of a quadratic annihilation operator and its adjoint is derived by means of a new method based on quantum white noise calculus. Our method consists of two steps: (i) to derive a system of differential equations consisting of quantum white noise derivatives and Wick products; and (ii) to solve explicitly the system of differential equations.

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