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

T. Paszkiewicz
^{a} and S. Wolski^{ b}^{a}Retired from Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, Rzeszów, Poland
^{b}Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, al. Powstańców Warszawy 6, PL-35959 Rzeszów, Poland |

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The numerical stability of the solution of recursion relation for mean occupation numbers derived by Schönhammer 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. |

DOI: 10.12693/APhysPolA.128.204 PACS numbers: 05.30.Fk, 03.75.Ss |