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Energy spectrum of two-particle scattering in a periodic box

Author

Listed:
  • Frank X. Lee

    (Physics Department, The George Washington University, Washington, DC 20052, USA)

  • Colin Morningstar

    (#x2020;Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA)

  • Andrei Alexandru

    (Physics Department, The George Washington University, Washington, DC 20052, USA)

Abstract

We aim to compute the discrete energy spectrum for two-body scattering in a three-dimensional box under periodic boundary conditions. The spectrum in the center of mass is obtained by solving the Schödinger equation in a test potential using the Fourier basis. The focus is on how to project the spectrum into the various irreducible representations of the symmetry groups of the box. Four examples are given to show how the infinite-volume spectrum (including both bound and scattering states) is resolved in cubic or elongated boxes, and in systems with integer or half-integer total spin. Such a demonstration is a crucial step in relating the discrete spectrum in the box to the infinite-volume scattering phaseshifts via the Lüscher method.

Suggested Citation

  • Frank X. Lee & Colin Morningstar & Andrei Alexandru, 2020. "Energy spectrum of two-particle scattering in a periodic box," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-44, September.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:09:n:s0129183120501314
    DOI: 10.1142/S0129183120501314
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