  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.

Quantum Physics