A Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for a Hydrogen Atom in the Magnetic Field: Cylindrical Coordinates

摘要: The boundary problem in cylindrical coordinates for the Schrodinger equation describing a hydrogen-like atom strong homogeneous magnetic field is reduced to set of longitudinal equations framework Kantorovich method. effective potentials these are given by integrals over transversal variable product transverse basis functions depending on as parameter and their first derivatives with respect parameter. A symbolic-numerical algorithm evaluating corresponding eigenvalues which depend parameter, corresponded presented. efficiency accuracy numerical scheme derived confirmed computations eigenenergies eigenfunctions low-excited states hydrogen field.