Integro-differential Schrödinger equation in the presence of a uniform magnetic field
Department of Physics, Faculty of Sciences, Salman Farsi University of Kazerun, 73175-457, Kazerun, Iran
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Accepted: 21 October 2016
Published online: 10 November 2016
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, , which is the function of magnitude and quantum number mL. We obtain the exact solution of the radial Schrödinger equation for mass function .
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016