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On the integration over operators composed of Dirac's symbols——beyond Newton-Leibniz integration over c-number functions

Fan Hong‐Yi

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

A new direction was proposed for developing NewtonLeibniz integration theory,i.e.integrations over Dirac's ket-bra operators of continuum variables in quantum mechanics.The necessity and feasibility of the integration over the operators of type | | were discussed,and further developing Dirac's symbolic method such that much more physical applications can be found.

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A new direction was proposed for developing NewtonLeibniz integration theory,i.e.integrations over Dirac's ket-bra operators of continuum variables in quantum mechanics.The necessity and feasibility of the integration over the operators of type | | were discussed,and further developing Dirac's symbolic method such that much more physical applications can be found.
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.