Fractional Schrödinger equation

2002/06/14 by Nick Laskin, N. Laskin · 16 citations
Chemistry · Mathematics · Physics and Astronomy · #Bohr model #Chemistry #Fractional Differential Equations Solutions #Fractional calculus #Mathematical physics #Mathematics #Operator (biology) #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Schrödinger equation #Semiclassical physics #Statistical Mechanics and Entropy #quant-ph

paper · pdf · doi:10.1103/physreve.66.056108

published as Phys.Rev.E66:056108,2002 · 18 pages

arxiv created 2002/06/14 · openalex publication_date 2002/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Some properties of the fractional Schrödinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrödinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schrödinger equations.

Citations

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• Fractional calculus [wikipedia]