On an effective approximation of the Kantorovich method for calculations of a hydrogen atom in a strong magnetic field

摘要

A new effective method of calculating the wave functions of discrete and continuous spectra of a hydrogen atom in a strong magnetic field is developed based on the Kantorovich approach to the parametric eigenvalue problems in spherical coordinates. The two-dimensional spectral problem for the Schroedinger equation with fixed magnetic quantum number and parity is reduced to a spectral parametric problem for a one-dimensional equation for. the angular variable and a finite set of ordinary second-order differential equations for the radial variable. A canonical transformation is applied to approximate the finite set of radial equations by means of a new radial equation describing an open channel. The rate of convergence is examined numerically and illustrated with a set of typical examples. The results are in good agreement with calculations by other authors.