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Abstract
The wave function for an electron in combined Coulomb and uniform magnetic fields is expanded in oblate speroidal angle functions. The resulting Schrodinger equation for the radial functions is solved in two regions of energy and magnetic field strength. First, for large "astrophysical" field strengths, two adiabatic methods are employed which yield rigorous upper and lower bounds on the lowest exact energy levels for each symmetry of the system. Results are presented for energies of hydrogenic ls and 2p levels in magnetic fields in the range 10('7 )(LESSTHEQ) B (LESSTHEQ) 10('11) Gauss. These results indicate that the present adiabatic methods employing spherical symmetry may be expected to give reliable results for energies of low-lying hydrogenic levels for magnetic fields in the range 0 (LESSTHEQ) B (LESSTHEQ) 10('9) G. Second, these adiabatic methods are used to obtain basis states for a calculation including non-adiabatic coupling. Properties of the oblate spheroidal eigenvalues and angle functions are presented, as are the properties of the matrix elements that couple the adiabatic channels. Results are presented for energy levels and oscillator strengths for transitions from the hydrogenic ground state to states with principal numbers 2 (LESSTHEQ) n (LESSTHEQ) 25 in laboratory-strength magnetic fields 8kG (LESSTHEQ) B (LESSTHEQ) 56kG. The effects of truncating the expansions needed in these calculations are found to be serious.
