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 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.

11 pages, 1 figure

References in corpus (4)

• Invariance of the correlation energy at high density and large dimension in two-electron systems
• Two-electron atoms, ions and molecules
• Semiclassical initial value calculations of collinear helium atom
• Two interacting electrons in a magnetic field: comparison of semiclassical, quantum, and variational solutions

Cited by in corpus (4)

• Effects of symmetry breaking in finite quantum systems
• Interacting electrons in a magnetic field in a center-of-mass free basis
• Transient capture of electrons in magnetic fields, or: comets in the restricted three-body problem
• Geometrical crossover in two-body systems in a magnetic field