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Numerical Solutions of the Bethe-Salpeter Equation

1969; American Institute of Physics; Volume: 187; Issue: 5 Linguagem: Inglês

10.1103/physrev.187.2051

1536-6065

W. B. Kaufmann,

Cold Atom Physics and Bose-Einstein Condensates

After summarizing the application of the Rayleigh-Ritz and Schwinger variational principles to the unequal-mass ${\ensuremath{\varphi}}^{3}$ Bethe-Salpeter equation, we present, in graphical and tabular form, the solution of the bound-state problem. The dependence of the coupling-parameter eigenvalue on the exchange mass, external mass ratio, and binding energy is examined in detail for $s$ and $p$ ground states. Mixing of excited levels leading to complex solutions is briefly studied, and some Regge trajectories are also calculated. Scattering phase shifts for unequal-mass scattering have been calculated and representative examples are given. The fact that certain levels do not appear to contribute to Levinson's theorem is also examined. Finally, the foregoing methods are generalized to two-channel systems, and channel phase shifts and inelasticities are computed.