On the spectrum of an oscillator in a magnetic field

2019/09/09 by Fernández, Francisco M.
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1909.04175

Abstract

We consider the Hamiltonian for a charged particle in a harmonic potential in the presence of a magnetic field. The most symmetric case depends on one parameter, the variation of which leads from a spectrum bounded from below to an unbounded spectrum. At the transition point the spectrum is bounded from below but each eigenvalue has infinite multiplicity. The algebraic method proves to be a remarkable tool for the analysis of this quadratic Hamiltonian.

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