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

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.