Time fractional Schrödinger equation
By M. Naber. 2004
479 citations recorded by the source corpus.
The Schrodinger equation is considered with the first order time derivative changed to a Caputo fractional derivative, the time fractional Schrodinger equation. The resulting Hamiltonian is found to be non-Hermitian and nonlocal in time. The resulting wave functions are thus not invariant under time reversal. The time fractional Schrodinger equation is solved for a free particle and for a potential well. Probability and the resulting energy levels are found to increase over time to a limiting value depending on the order of the time derivative. New identities for the Mittag–Leffler function are also found and presented in an Appendix.
Subfields: Atomic and Molecular Physics, and Optics, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/aa423a72d6990f29640763813fbcd982a541813a
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In Atomic and Molecular Physics, and Optics
In Modeling and Simulation
In Statistical and Nonlinear Physics
Citations in the corpus
- A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives (2010, methodology): “Despite of the above mentioned properties, the fractional calculus was used, as a powerful tool, for solving various problems involving the non-locality inmany fields in both science and engineering (see for example, [7–16] and the references therein).”
- A new Definition of Fractional Derivative without Singular Kernel (2015, unknown): “Laskin [21], Naber [22], Baleanu et al.”
- New results on stability and stabilization of a class of nonlinear fractional-order systems (2013, background): “It is therefore that many real-world physical systems are well characterized by fractional-order state equations [1–4], for example, fractional-order Schrödinger equation [5] in quantum mechanics, fractional-order oscillator equation [6] in damping vibration, fractional Lotka–Volterra equation [7] i”