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Semi-relativistic wave-phase approximation for two-body spinless bound states in 1+1 dimensions | | K.-E. Thylwe
; S. Belov
; | | Date: |
9 Aug 2015 | | Abstract: | An approximate quantum-mechanical two-body equation for spinless particles
incorporating relativistic kinematics is derived. The derivation is based on
the relativistic energy-momentum relation $mc^{2}+epsilon =
sqrt{m^{2}c^{4}+p^{2}c^{2}}+V$ for each single particle, where $mc^2$ is the
particle rest mass energy, $p$ its linear momentum, $epsilon$ its dynamical
energy, and $V$ being the time-like vector interaction potential. The resulting
two-body equation assumes rapid wave oscillations in a single, slowly varying
potential well. A Bohr-Sommerfeld-type quantization condition is obtained. The
approximation is compared to exact results for the harmonic potential. | | Source: | arXiv, 1508.2067 | | Services: | Forum | Review | PDF | Favorites | |
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