Integro-differential Schrödinger equation in the presence of a uniform magnetic field

Abstract.

The integro-differential Schrödinger equation (IDSE) was introduced by physicists to investigate nuclear reactions. In this work, we investigate the integro-differential Schrödinger equation in the presence of a uniform magnetic field. We show how the three-dimensional IDSE will be changed to a velocity-dependent Schrödinger equation in the presence of a uniform magnetic field. We find that interaction Hamiltonian will become a three-dimensional Schrödinger equation with the position-dependent effective mass, m(r), and potential energy, $U^{\prime}_{m}(r)$, which is the function of magnitude $\mathbf{r}$ and quantum number m_L. We obtain the exact solution of the radial Schrödinger equation for mass function $M(r)= \frac{1}{(1+\gamma^{2}r^{2})^{2}}$.