Numerical Stability of Solution of Recursion Relation for Ideal Quantum Gases Containing Finite Number of Harmonically Trapped Particles

摘要

The numerical stability of the solution of recursion relation for mean occupation numbers derived by Schonhammer for ideal Fermi gas trapped in 1D harmonic potential is studied. In low temperature region there exists a solution of this recursion relation. In high temperature region the iteration becomes unstable. In low and high temperature regions with growing number of particles the region of numerical instability diminishes.