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

Abstract

The integro-differential Schrodinger equation (IDSE) was introduced by physicists to investigate nuclear reactions. In this work, we investigate the integro-differential Schrodinger equation in the presence of a uniform magnetic field. We show how the three-dimensional IDSE will be changed to a velocity-dependent Schrodinger equation in the presence of a uniform magnetic field. We find that interaction Hamiltonian will become a three-dimensional Schrodinger 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 mL. We obtain the exact solution of the radial Schrodinger equation for mass function \( M(r)= \frac{1}{(1+\gamma^{2}r^{2})^{2}}\).