Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Abstract

For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman–Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with a Langer correction. The latter are restricted to integrable systems, however, whereas the time-dependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential.