The spectrum of coherent modes for dilute atomic Bose gas, confined in a non-isotropic harmonic trap, is determined by using the optimized perturbation theory and the technique of self-similar root approximants. The obtained expressions are valid for arbitrary energy levels of all excited nonlinear coherent modes. This article must be used as an introduction for the students that want to deepen nowadays in the theme of the Bose-Einstein condensation.
Bose trapped gases; energy spectrum; optimezed perturbation theory
