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 $δ$-potential well defined by $V(x) =- γδ^{\la}(x)$, where $γ>0$ 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.
Bound states in the continuum of fractional Schrödinger equation in the Earth's gravitational field and their effects in the presence of a minimal length: applications to distinguish ultralight particles
Time independent fractional Schrodinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative
Multiparticle localization for disordered systems on continuous space via the fractional moment method
本文研究了在$ \mathbb{R}^d $上的$ n $粒子量子系统的光谱和动力学局域化，该系统受随机势的作用，并通过一个可能具有无限范围的对势相互作用。我们建立了两个条件，以确保频谱和动力学本地化附近的底部的$ n $ -粒子系统的频谱：i）本地化建立在制度的弱相互作用假设一个粒子本地化，和ii）本地化也建立在一个Lifshitz尾型条件下的稀疏性的频谱。在多项式衰减的相互作用的情况下，我们提供了一个上限的粒子的数量，这些条件适用。
