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

Details Solutions of a particle with fractional $δ$-potential in a fractional dimensional space Solutions of a particle with fractional $δ$-potential in a fractional dimensional space

2010-01-25

arxiv.org/abs/1001.4352v2

Physics

Mathematical Physics

Scientific paper

A Fourier transformation in a fractional dimensional space of order $\la$ ($0<\la\leq 1$) is defined to solve the Schr\"odinger equation with Riesz fractional derivatives of order $\a$. This new method is applied for a particle in a fractional $\delta$-potential well defined by $V(x) =- \gamma\delta^{\la}(x)$, where $\gamma>0$ and $\delta^{\la}(x)$ 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.

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