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arXiv · 1508.02067

Semi-relativistic wave-phase approximation for two-body spinless bound states in 1+1 dimensions

K. -E. Thylwe·S. Belov
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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.

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K. -E. Thylwe, S. Belov. 2015-08-09. Semi-relativistic wave-phase approximation for two-body spinless bound states in 1+1 dimensions. https://arxiv.org/abs/1508.02067

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