New approach for deriving operator identities by alternately using normally, antinormally, and Weyl ordered integration

2009/10/15 by Hong-Yi Fan, Hong-yi Fan, Fan, Hong-yi +2 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #Mechanical and Optical Resonators #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.0910.2850

6 figures, submitted to Am. J. Phys

arxiv created 2009/10/15 · openalex publication_date 2009/10/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dirac's ket-bra formalism is the "language" of quantum mechanics and quantum field theory. In Refs.(Fan et al, Ann. Phys. 321 (2006) 480; 323 (2008) 500) we have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra projectors. In this work by alternately using the technique of integration within normal, antinormal, and Weyl ordering of operators we not only derive some new operator ordering identities, but also deduce some useful integration formulas regarding to Laguerre and Hermite polynomials. This opens a new route of deriving mathematical integration formulas by virtue of the quantum mechanical operator ordering technique.

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