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 0 2r 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.
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