Lattice two-body problem with arbitrary finite-range interactions

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.042102· OSTI ID:21408557

Valiente, Manuel ^[1]

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1. Institute of Electronic Structure and Laser, FORTH, GR-71110 Heraklion, Crete (Greece)

We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering states, and the ''low-energy'' solutions by very efficient and easy-to-implement numerical means. All bound states are proven to be characterized by roots of a polynomial whose degree depends linearly on the range of the potential, and we discuss the connections between the number of bound states and the scattering lengths. ''Low-energy'' resonances can be located with great precision with the methods we introduce. Further generalizations to include more exotic interactions are also discussed.

• OSTI ID: 21408557
• Journal Information: Physical Review. A, Vol. 81, Issue 4; Other Information: DOI: 10.1103/PhysRevA.81.042102; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ACCURACY
BOUND STATE
EXACT SOLUTIONS
FINITE-RANGE INTERACTIONS
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
POTENTIALS
RESONANCE
SCATTERING
SCATTERING LENGTHS
SPECTRA
TWO-BODY PROBLEM
DIMENSIONS
FUNCTIONS
INTERACTIONS
LENGTH
MANY-BODY PROBLEM
MATHEMATICAL SOLUTIONS