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2019 Existence of propagators for time-dependent Coulomb-like potentials
Eric Stachura
Rocky Mountain J. Math. 49(7): 2347-2374 (2019). DOI: 10.1216/RMJ-2019-49-7-2347

Abstract

We prove existence of propagators for a time-dependent Schrodinger 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 discuss various properties and applications related to the essential spectrum of the Hamiltonian associated to these potentials.

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Eric Stachura. "Existence of propagators for time-dependent Coulomb-like potentials." Rocky Mountain J. Math. 49 (7) 2347 - 2374, 2019. https://doi.org/10.1216/RMJ-2019-49-7-2347

Information

Published: 2019
First available in Project Euclid: 8 December 2019

zbMATH: 07152868
MathSciNet: MR4039973
Digital Object Identifier: 10.1216/RMJ-2019-49-7-2347

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 7 • 2019
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