Initial Value Problem for a Caputo Space-time Fractional Schrodinger Equation for the Delta Potential

TL;DR

This paper solves a Caputo space-time fractional Schrödinger equation with delta potential using Laplace and Fourier transforms, deriving wave functions and energy eigenvalues for a particle in this potential.

Contribution

It introduces a method to solve fractional Schrödinger equations with delta potentials, providing explicit solutions for wave functions and energy levels.

Findings

Wave function expressions for the fractional Schrödinger equation

Energy eigenvalues for the delta potential case

Application of Laplace and Fourier transforms to fractional quantum problems

Abstract

In this paper, we investigate the initial value problem for a Caputo space-time fractional Schrodinger equation for the delta potential. To solve this equation, we use the joint Laplace transform on the spatial coordinate and the Fourier transform on the time coordinate. Finally, the wave function and the time dependent energy eigenvalues are obtained for a particle which is subjected to the delta potential.