Discrete variable representation for highly excited states of hydrogen atoms in magnetic fields

A discrete variable representation (DVR) appropriate for describing the highly excited states of hydrogen atoms in laboratory-strength magnetic fields is constructed by using a symmetry-adapted direct product of one-dimensional DVR's in parabolic coordinates related to generalized Gauss-Laguerre quadratures. The resulting sparse Hamiltonian matrix is used in an iterative (filter-diagonalization) procedure to obtain eigenvalues and eigenvectors in a given spectral domain. The method is applied to calculate eigenvalues and lifetimes of ``circular'' Rydberg states, as well as oscillator strengths for the excitation of highly excited states.