Numerical analysis of Bose–Einstein condensation in a three-dimensional harmonic oscillator potential

Bose–Einstein condensation is the anomalous accumulation of particles in the ground state of a system of bosons, when compared with the population in a system of particles obeying classical statistics. I use undergraduate-level statistical mechanics and a symbolic algebra computer program to study the occupation numbers of the energy levels of a finite number of noninteracting particles confined in a three-dimensional harmonic oscillator potential. I also calculate the heat capacity of the gas. The harmonic oscillator potential simplifies the calculations and approximates the conditions of the recent experiments achieving Bose–Einstein condensation in laser-cooled alkali vapors. © 1998 American Association of Physics Teachers.