Energy spectrum of two-particle scattering in a periodic box

Frank X. Lee, Colin Morningstar () and Andrei Alexandru ()
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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

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 09, 1-44

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.

Keywords: Two-body scattering; cubic and elongated boxes; periodic boundary conditions; Fourier basis; irreducible representations (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120501314

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