SO(2, 1) algebra and the large N expansion in quantum mechanics
Abstract
We discuss the large N expansion in quantum mechanics using an algebraic procedure based on a Holstein-Primakoff representation of the well-known SO(2, 1) algebra. Both spherically and axially symmetric potentials are studied. The method is explicitly illustrated for the family of potentials V = ω 02r 2/2 + 2νr 2ν as well as the hydrogen atom in a uniform magnetic field. In the latter case, the first non-trivial iteration of the present perturbative scheme yields accurate results for the energy levels, even for strong magnetic field intensities. Further generalizations and applications are outlined.
- Publication:
-
Annals of Physics
- Pub Date:
- September 1980
- DOI:
- 10.1016/0003-4916(80)90323-1
- Bibcode:
- 1980AnPhy.128..314M