For 10 points, name this quantum system, a generalization of a mass on a spring.
Shifting the states of this system by x-sub-0 corresponds to the energy levels of cyclotron orbits in Landau quantization. A constant times the exponent of negative q squared over 2 gives the psi-sub-zero of this system, whose coherent states are named for Glauber. A pair of matrices whose superdiagonal and subdiagonal elements are the square roots of the natural numbers are used to move between (*) energy levels of this system; those are symbolized a and a-dagger and are called the ladder operators. The energies of this system, whose wavefunctions contain the Hermite polynomials, are spaced h-bar times omega, and its potential is given by Hooke's law. For 10 points, name this quantum system, a generalization of a mass on a spring.
Shifting the states of this system by x-sub-0 corresponds to the energy levels of cyclotron orbits in Landau quantization.
quantum harmonic oscillator [or QHO; prompt on “oscillator”, “harmonic oscillator” or “simple harmonic oscillator”]