Algebraic Perturbation Theory for Hydrogen Atom in Weak Electric Fields
Programming and Computing Software
A Comparison of Algorithms for the Normalization and Quantization of Polynomial Hamiltonians
Programming and Computing Software
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Programming and Computing Software
Symbolic-numeric algorithms for computer analysis of spheroidal quantum dot models
CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Hi-index | 0.00 |
A symbolic-numerical algorithm for the computation of the matrix elements in the parametric eigenvalue problem to a prescribed accuracy is presented. A procedure for calculating the oblate angular spheroidal functions that depend on a parameter is discussed. This procedure also yields the corresponding eigenvalues and the matrix elements (integrals of the eigenfunctions multiplied by their derivatives with respect to the parameter). The efficiency of the algorithm is confirmed by the computation of the eigenvalues, eigenfunctions, and the matrix elements and by the comparison with the known data and the asymptotic expansions for small and large values of the parameter. The algorithm is implemented as a package of programs in Maple-Fortran and is used for the reduction of a singular two-dimensional boundary value problem for the elliptic second-order partial differential equation to a regular boundary value problem for a system of second-order ordinary differential equations using the Kantorovich method.