28 research outputs found
Solutions of a particle with fractional -potential in a fractional dimensional space
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 -potential well defined by V(x) =-
\gamma\delta^{\la}(x), where 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