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Quantum mechanics and nilpotent groups. I: The curved magnetic field. (English) Zbl 0601.58027
The authors consider quantum mechanical systems whose Hamiltonians are quadratic in generators of a nilpotent Lie algebra. The physical examples of such systems involve massive spinless particles in external magnetic fields (constant and linear in space variables). Using the group representation method the spectrum of such systems is found. The explicit time dependence of the system is also found using the representation structure of nilpotent groups. The approach developed in this article is very close to the coherent states method.
Reviewer: M.Monastyrsky

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
22E25 Nilpotent and solvable Lie groups
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
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