Simple and accurate calculations on a Lagrange mesh of the hydrogen atom in a magnetic field

Five easily reproducible calculations on a mesh of the hydrogen atom in a magnetic field using three different coordinate systems are described. The calculations are performed with the Lagrange- mesh method, an approximate variational method resembling a mesh method and providing very accurate energies and wavefunctions. Highly accurate energies agreeing with the series expansion results are obtained for the lowest m = 0 to - 10 states in magnetic fields gamma = 1, 10, 100 and 1000. These calculations are easily reproducible in short computation times. The root- mean- square radius and the quadrupole moment are computed with high accuracy and discussed. The first and second positive- parity excited states and the lowest negative- parity state are also considered for m = 0. In all cases, the accuracy decreases with increasing fields.