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

TL;DR

This paper demonstrates that semiclassical initial value methods can accurately compute spectra of a two-electron quantum dot in a magnetic field, offering advantages over traditional WKB approaches especially for complex, high-dimensional systems.

Contribution

It introduces a time-dependent semiclassical approach using the Herman-Kluk propagator for spectral calculations in quantum dots, extending applicability beyond integrable systems.

Findings

Semiclassical methods achieve accuracy comparable to WKB with Langer correction.

The approach is applicable to high-dimensional and potentially chaotic systems.

It allows for arbitrary potential shapes in spectral calculations.

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.