Semiclassical wave functions and energy levels of Bose-condensed gases in spherically symmetric traps

TL;DR

This paper develops a semiclassical WKB-approximation for Bogoliubov equations in Bose-condensed gases within spherical traps, providing analytical and numerical insights into excitation spectra and energy level shifts near the condensate surface.

Contribution

It introduces a semiclassical quantization approach for Bogoliubov excitations in spherically symmetric Bose gases, including analytical and numerical analysis of energy levels.

Findings

Energy levels can be significantly shifted near the condensate surface.

The quantization rule is based on a Bohr-Sommerfeld type approximation.

Numerical and analytical spectra are consistent in certain limits.

Abstract

The WKB-approximation for the Bogoliubov-equations of the quasi-particle excitations in Bose-gases with condensate is worked out in the case of spherically symmetric trap potentials on the basis of the resulting quantization rule. The excitation spectrum is calculated numerically and also analytically in certain limiting cases. It is found that the energy levels of a Bohr-Sommerfeld type quantization may be considerably shifted when the classical turning point gets close to the surface of the condensate.