Electromagnetic transitions of the hydrogen atom in a magnetic field by the Lagrange-mesh method

Very accurate wavefunctions obtained with the Lagrange-mesh method are employed to calculate dipole strengths and the dominant quadrupole strength in the high-field domain (γ ≥ 1) within the infinite-proton-mass approximation. Calculations are performed in the semi-parabolic and spherical coordinate systems. The accuracy is tested by varying the number of mesh points and by comparison between both coordinate systems. Comparison between the position (or length) and velocity expressions of the dipole strength is found not to be a reliable test as it overestimates the accuracy. We confirm that published tables have in general a four-digit accuracy. The Lagrange-mesh technique provides a simple and fast way of obtaining similar results at arbitrary fields with γ ≤ 1000. Using the semi-parabolic coordinate system is simpler and more robust.