A symbolic-numerical algorithm for solving the eigenvalue problem for a hydrogen atom in the magnetic field: Cylindrical coordinates. (English) Zbl 1141.68680

Ganzha, Victor G. (ed.) et al., Computer algebra in scientific computing. 10th international workshop, CASC 2007, Bonn, Germany, September 16–20, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-75186-1/pbk). Lecture Notes in Computer Science 4770, 118-133 (2007).
Summary: The boundary problem in cylindrical coordinates for the Schrödinger equation describing a hydrogen-like atom in a strong homogeneous magnetic field is reduced to the problem for a set of the longitudinal equations in the framework of the Kantorovich method. The effective potentials of these equations are given by integrals over transversal variable of a product of transverse basis functions depending on the longitudinal variable as a parameter and their first derivatives with respect to the parameter. A symbolic-numerical algorithm for evaluating the transverse basis functions and corresponding eigenvalues which depend on the parameter, their derivatives with respect to the parameter and corresponded effective potentials is presented. The efficiency and accuracy of the algorithm and of the numerical scheme derived are confirmed by computations of eigenenergies and eigenfunctions for the low-excited states of a hydrogen atom in the strong homogeneous magnetic field.
For the entire collection see [Zbl 1138.68004].


68W30 Symbolic computation and algebraic computation


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