On the spectrum of an oscillator in a magnetic field

Francisco M. Fernández

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arXiv · 1909.04175

On the spectrum of an oscillator in a magnetic field

Francisco M. Fernández

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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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Francisco M. Fernández. 2019-09-09. On the spectrum of an oscillator in a magnetic field. https://arxiv.org/abs/1909.04175

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