Existence of Propagators for Time Dependent Coulomb-like Potentials

Autor:	Stachura, Eric
Rok vydání:	2017
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs Quantum Physics 35Q41 82C03 81Q10
Druh dokumentu:	Working Paper
Popis:	We prove existence of propagators for a time dependent Schr\"odinger equation with a new class of softened Coulomb potentials, which we allow to be time dependent, in the context of time dependent density functional theory. We compute explicitly the Fourier transform of these new potentials, and provide an alternative proof for the Fourier transform of the Coulomb potential using distribution theory. Finally we show the new potentials are dilatation analytic, and so the spectrum of the corresponding Hamiltonian can be fully characterized. Comment: More references added; two brief remarks added in Section 3 and Section 6, results unchanged
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.06166 Zobrazit plný text záznamu View this record from Arxiv