Abstract.
A complex harmonic-oscillator basis is employed for the three-body problem obeying S 3-symmetry. Unlike a real basis it generates an additional quantum number (N a ), in addition to the standard principal quantum number (N), and thus facilitates a more quantitative S 3-classification of the various states than is usually possible. It is shown that certain bilinear forms with definite S 3-symmetry properties, which can be constructed out of the linear harmonic-oscillator operators (a, a †) satisfy several uncoupled sets of SO(2, 1) algebras with spectra bounded from below. It is also briefly indicated how this S 3-formalism can be adapted to the core structure of a more general relativistic three-particle system with unequal-mass kinematics through an appropriate choice of internal variables.
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Received May 11, 1994; revised November 3, 1994; accepted for publication November 23, 1994
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Mitra, A., Sharma, A. & Mitra-Sodermark, B. Complex Harmonic-Oscillator Basis for the Relativistic Three-Body Problem. Few-Body Systems 19, 145–156 (1995). https://doi.org/10.1007/s006010050022
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DOI: https://doi.org/10.1007/s006010050022