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Perturbative Solutions Of Quantum Mechanical Problems By Symbolic Computation: A Review

Author

Listed:
  • T. C. SCOTT

    (Guelph-Waterloo Program for Graduate Work in Physics, Waterloo Campus, Canada)

  • R. A. MOORE

    (Guelph-Waterloo Program for Graduate Work in Physics, Waterloo Campus, Canada)

  • G. J. FEE

    (Department of Computer Science University of Waterloo, Waterloo, Ontario, N2L-3G1, Canada)

  • M. B. MONAGAN

    (Department of Computer Science University of Waterloo, Waterloo, Ontario, N2L-3G1, Canada)

  • G. LABAHN

    (Department of Computer Science University of Waterloo, Waterloo, Ontario, N2L-3G1, Canada)

  • K. O. GEDDES

    (Department of Computer Science University of Waterloo, Waterloo, Ontario, N2L-3G1, Canada)

Abstract

It is shown that Symbolic Computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The method presented herein solves for both the eigenfunctions and eigenenergies as power series in the order parameter where each coefficient of the perturbation series is obtained in closed form. The algorithms are expressed in the Maple symbolic computation system but can be implemented on other systems. This approach avoids the use of an infinite basis set and some of the complications of degenerate perturbation theory. It is general and can, in principle, be applied to many separable systems.

Suggested Citation

  • T. C. Scott & R. A. Moore & G. J. Fee & M. B. Monagan & G. Labahn & K. O. Geddes, 1990. "Perturbative Solutions Of Quantum Mechanical Problems By Symbolic Computation: A Review," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 53-76.
    • Handle: RePEc:wsi:ijmpcx:v:01:y:1990:i:01:n:s0129183190000037
    DOI: 10.1142/S0129183190000037
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