We present the recent results of our continuing program of investigation of the behavior of matter in strong to super-strong magnetic fields (B∼ 106−1012G). This work was motivated by the discovery of strong magnetic fields (B∼ 107G) in some white dwarfs and the likely existence of super-strong fields (B∼ 1012G) in pulsars. Magnetic white dwarfs were discovered from observations of the continuous spectrum and one of the most intriguing challenges for the theorist is to provide an explanation

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... the observed wavelength dependence of the fractional circularly and linearly polarized radiation. Our initial response to this question was the determination of an exact solution of Kemp's harmonic oscillator model. These results are used as input to the ATLAS model atmosphere program and then comparison is made with observations. The disparities still existing between theory and observation convince us of the necessity for developing a new model of the continuum radiation, two likely possibilities being photoionization and free-free absorption. This leads us to present a general formulation of radiation absorption and emission processes in a magnetic field. Next we calculate the cross section for the photoionization, correct to first order inB. For the purpose of obtaining exact results for this cross section, the effect of a magnetic field on the energy spectrum and wave functions of hydrogen, helium, etc. must be obtained. The results for hydrogen are presented here. They will be useful also in determining accurate values for the displacements due to the quadratic Zeeman effect in the line spectra of DA stars, particularly for the higher excited states.