Quantitative and qualitative analysis of Bose-Einstein condensation in harmonic traps

A simple and direct-approach to handle summation is presented., With this approach, we analytically investigate Bose-Einstein condensation of ideal Bose gas trapped in an isotropic harmonic oscillator potential. We get the accurate expression of T. which is very close to (0.43% larger than) the experimental data. We find the curve of internal energy of the system vs. temperature has a turning point which marks the beginning of a condensation. We also find that there exists specific heat jump at the transition temperature, no matter whether the system is macroscopi. c or finite. This phenomenon could be a manifestation of a phase transition in unite systems.