Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well

DOI10.1063/1.4894057zbMath1304.81069arXiv1403.5668OpenAlexW3098058822MaRDI QIDQ2924881

Piotr Garbaczewski, Mariusz Żaba

Publication date: 20 October 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5668

zbMATH Keywords

spectral problemsStrang methodCauchy oscillatorCauchy wellnonl-ocal Schrödinger operator

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Fractional partial differential equations (35R11)

Related Items (7)

Stabilization of fundamental solitons in the nonlinear fractional Schrödinger equation with \(\text{PT}\)-symmetric nonlinear lattices ⋮ On the coherent states for a relativistic scalar particle ⋮ Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement ⋮ Nonlocally induced (fractional) bound states: Shape analysis in the infinite Cauchy well ⋮ Effective approximation for a nonlocal stochastic Schrödinger equation with oscillating potential ⋮ Fourier pseudospectral method for fractional stationary Schrödinger equation ⋮ Brownian motion in trapping enclosures: steep potential wells, bistable wells and false bistability of induced Feynman–Kac (well) potentials

Cites Work

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• Applications of continuity and discontinuity of a fractional derivative of the wave functions to fractional quantum mechanics

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