Journal article
Quantum Mechanics and Nilpotent Groups. I. The Curved Magnetic Field
Publications of the Research Institute for Mathematical Sciences, Vol.21(5), pp.969-999
1985
DOI: 10.2977/prims/1195178792
Abstract
The quantum mechanics of massive spinless particles in an external magnetic field polynomial in position variables is shown to be related to nilpotent Lie groups. By using the known representation structure of such groups, the Hilbert spaces of the quantum mechanical systems can be decomposed into irreducible representations of the nilpotent groups. Such a decomposition is given explicitly for constant and curved magnetic fields. Since the Hamiltonian for polynomial magnetic fields is quadratic in the Lie algebra elements, its spectrum can be found using the representation structure of nilpotent groups. The explicit time dependence of the system can also be found by solving the heat equation on nilpotent groups. These ideas are worked out for the constant magnetic field, where the solution is well known, and the curved magnetic field, where it is not. Generalizations to other systems whose interaction terms are polynomial are also given.
Details
- Title: Subtitle
- Quantum Mechanics and Nilpotent Groups. I. The Curved Magnetic Field
- Creators
- Palle Jorgensen - University of Iowa, IOWA CITY, UNITED STATESW Klink - University of Iowa, IOWA-CITY, UNITED STATES
- Resource Type
- Journal article
- Publication Details
- Publications of the Research Institute for Mathematical Sciences, Vol.21(5), pp.969-999
- Publisher
- European Mathematical Society Publishing House; Zuerich, Switzerland
- DOI
- 10.2977/prims/1195178792
- ISSN
- 0034-5318
- eISSN
- 1663-4926
- Language
- English
- Date published
- 1985
- Academic Unit
- Mathematics; Physics and Astronomy
- Record Identifier
- 9983985814702771
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