St-Petersburg State University Research Institute of Physics Faculty of Physics High Energy and Elementary Particles Physics
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Mikhail V. Ioffe
Ioffe Mikhail Vul'fovich
Doctor of Science (Habilitation) in Theoretical and Mathematical Physics - 1996
In the Doctor (Habilitation) thesis "Supersymmetrical Method in Quantum Mechanics and Multidimensional Quantum Systems with Equivalent spectra " a new approach in Supersymmetrical Quantum Mechanics was proposed, which allowed to study the wide class of multidimensional quantum systems by means of supersymmetry. The well-known Darboux-Crum transformation was generalized onto the case of arbitrary dimensionality of space. The notion of polynomial supersymmetry, which includes both reducible and irreducible Darboux transformations, was introduced. The wide new class of integrable two-dimensional systems, which are not amenable to separation of variables, was constructed. The supersymmetric approach was used to investigate the spectra of nonrelativistic half spin particle in external electromagnetic fields. Method of supersymmetry was applied to study the scattering problem for multidimensional and multi-channel systems.
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March 2009