Quantum mechanics and nilpotent groups. I: The curved magnetic field
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.
scientific article; zbMATH DE number 3969707