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arXiv · 1605.04321

Generalized Delta Functions and Their Use in Quantum Optics

R. A. Brewster·J. D. Franson
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Abstract

The Dirac delta function is widely used in many areas of physics and mathematics. Here we consider the generalization of a Dirac delta function to allow the use of complex arguments. We show that the properties of a generalized delta function are very different from those of a Dirac delta function and that they behave more like a pole in the complex plane. We use the generalized delta function to derive the Glauber-Sudarshan P-function for a Schr\"odinger cat state in a surprisingly simple form. Aside from their potential applications in classical electromagnetism and quantum optics, these results provide insight into the ability of the diagonal P-function to describe density operators with off-diagonal elements.

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R. A. Brewster, J. D. Franson. 2016-05-13. Generalized Delta Functions and Their Use in Quantum Optics. https://doi.org/10.1063/1.4985938

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