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Some physical applications of fractional Schrödinger equation. (English) Zbl 1112.81028
Summary: The fractional Schrödinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schrödinger equation, the Green’s function of the Lippmann-Schwinger integral equation is given.
MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
35Q40PDEs in connection with quantum mechanics
81U052-body potential scattering theory (quantum theory)