Magnetized hydrogen atom on a Laguerre mesh

Without any analytic calculation of a matrix element, energies and root-mean-square radii of the hydrogen atom in low and intermediate magnetic fields are calculated with high accuracy. With the Lagrange functions technique, the Schroedinger equation in semiparabolic coordinates is discretized on a small modified Laguerre mesh involving ten points for each coordinate. The mesh equations approximate a variational calculation with at most 55 basis functions. For a reduced field γ = 0.001 or 0.01, the accuracy of the energies is better than 10-12 for a number of low-lying m = 0 and ±1 states of both parities. At γ = 0.1, the accuracy starts decreasing beyond the second excited state because the dominant spherical symmetry of the basis becomes less appropriate. (author)