Fractional Schrödinger equation
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- 18 November 2002
- journal article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 66 (5) , 056108
- https://doi.org/10.1103/physreve.66.056108
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.Keywords
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This publication has 10 references indexed in Scilit:
- The random walk's guide to anomalous diffusion: a fractional dynamics approachPublished by Elsevier ,2000
- Fractional quantum mechanicsPhysical Review E, 2000
- Fractional quantum mechanics and Lévy path integralsPublished by Elsevier ,2000
- Quantum Lévy PropagatorsThe Journal of Physical Chemistry B, 2000
- Fractional kinetic equations: solutions and applicationsChaos: An Interdisciplinary Journal of Nonlinear Science, 1997
- Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy FlightPhysical Review Letters, 1994
- L'intégrale de Riemann-Liouville et le problème de CauchyActa Mathematica, 1949
- LXXIII. On the constitution of atoms and moleculesJournal of Computers in Education, 1913
- XXXVII. On the constitution of atoms and moleculesJournal of Computers in Education, 1913
- I. On the constitution of atoms and moleculesJournal of Computers in Education, 1913