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    Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force

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    The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

    New Mechanism of Magnetoresistance in Bulk Semiconductors: Boundary Condition Effects

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    We consider the electronic transport in bounded semiconductors in the presence of an external magnetic field. Taking into account appropriate boundary conditions for the current density at the contacts, a change in the magnetoresistance of bulk semiconductors is found as compared with the usual theory of galvanomagnetic effects in boundless media. New mechanism in magnetoresistance connected with the boundary conditions arises. In particular, even when the relaxation time is independent of the electron energy, magnetoresistance is not vanish.Comment: 7 pages, Elsart macro package (LaTeX2e edition
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