The Kantorovich method for high-accuracy calculations of a hydrogen atom in a strong magnetic field: low-lying excited states

Abstract

A new high-accuracy method for calculating the energy values of low-lying excited states of a hydrogen atom in a strong magnetic field (0 ⩽ B ⩽ 1013G) is developed based on the Kantorovich approach to parametric eigenvalue problems and using the axial symmetry. The initial two-dimensional spectral problem for the Schrödinger equation is reduced to a spectral parametric problem for a one-dimensional equation and a finite set of ordinary second-order differential equations. The rate of convergence is examined numerically and is illustrated with a set of typical examples. The results are in good agreement with precise calculations by other authors.