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.
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Guo et al. (2006) studied this question.
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