2016/03/17 by J. Julve, Julve, J., Ricardo Cepedello +5
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum optics and atomic interactions #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1603.05530
8 pages, 3 figures
arxiv created 2016/03/17 · openalex publication_date 2016/03/17 · arxiv updated 2016/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The extension of the Dirac Delta distribution (DD) to the complex field is needed for dealing with the complex-energy solutions of the Schrödinger equation, typically when calculating their inner products. In quantum scattering theory the DD usually arises as an integral representation involving plane waves of real momenta. We deal with the complex extension of these representations by using a Gaussian regularization. Their interpretation as distributions requires prescribing the integration path and a corresponding space of test functions. An extension of the Sokhotski-Plemelj formula is obtained. This definition of distributions is alternative to the historic one referred to surface integrations on the complex plane.