Solutions of a particle with fractional $\delta$-potential in a fractional dimensional space

Abstract

A Fourier transformation in a fractional dimensional space of order $\la$ ($0<\la\leq 1$) is defined to solve the Schrödinger equation with Riesz fractional derivatives of order $\a$. This new method is applied for a particle in a fractional $\delta$-potential well defined by $V(x) =- γδ^{\la}(x)$, where $\gamma >0$ and $δ^{\la}(x)$ is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if $0< \la<\a$. The results for $\la= 1$ and $\a=2$ are in exact agreement with those presented in the standard quantum mechanics.

References in corpus (5)

• Fractional Quantum Mechanics
• Time fractional Schrodinger equation
• Fractional Hydrodynamic Equations for Fractal Media
• Electromagnetic Fields on Fractals
• Gravitational Field of Fractal Distribution of Particles

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