Journal article
Spectral transform for the sub-Laplacian on the Heisenberg group
Journal d'analyse mathématique (Jerusalem), Vol.50(1), pp.101-121
12/1988
DOI: 10.1007/BF02796116
Abstract
We continue our analysis of nilpotent groups related to quantum mechanical systems whose Hamiltonians have polynomial interactions. For the spinless particle in a constant external magnetic field, the associated nilpotent group is the Heisenberg group. We solve the heat equation for the Heisenberg group by diagonalizing the sub-Laplacian. The unitary map to the Hilbert space in which the sub-Laplacian is a multiplication operator with positive spectrum is given. The spectral multiplicity is shown to be related to the irreducible representations of SU(2). A Lax pair, generated from the Heisenberg sub-Laplacian, is used to find operators unitarily equivalent to the sub-Laplacian, but not arising from the SL(2,R) automorphisms of the Heisenberg group.
Details
- Title: Subtitle
- Spectral transform for the sub-Laplacian on the Heisenberg group
- Creators
- Palle E. T JorgensenWilliam H Klink
- Resource Type
- Journal article
- Publication Details
- Journal d'analyse mathématique (Jerusalem), Vol.50(1), pp.101-121
- DOI
- 10.1007/BF02796116
- ISSN
- 0021-7670
- eISSN
- 1565-8538
- Language
- English
- Date published
- 12/1988
- Academic Unit
- Mathematics; Physics and Astronomy
- Record Identifier
- 9983985858102771
Metrics
15 Record Views