angular momenta or energy in a particular range in Reissner-Nordstroem geometry, there exist classically forbidden regions on the outside of

the respective event horizons which scatter certain in-falling geodesics or screen some of the black holes' evaporation by reflecting the emitted

particles back into the black holes. Quantum tunneling across this forbidden regions is studied. ]]>

operators and general potentials. We provide a criteria for the existence of multiple

solutions to these equations. As special cases we get the classical results on

existence of innitely many distinct solutions within Hartree and Hartree-Fock

theory of atoms and molecules subject to an external magnetic fields. We also

extend recent results within this theory, including Coulomb system with a constant

magnetic field, a decreasing magnetic field and a "physically measurable" magnetic field.

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