Study of Time Evolution for Approximation of Two-Body Spinless-Salpeter Equation
Hadi Sobhani, Hassan Hassanabadi
TL;DR
This paper develops a semi-relativistic approach using the Lewis-Riesenfeld invariant method to analyze the time evolution of the two-body spinless Salpeter equation in the heavy quark limit.
Contribution
It introduces a novel application of the Lewis-Riesenfeld invariant method to the time-dependent two-body spinless Salpeter equation in the heavy quark approximation.
Findings
Derived the time evolution operator for the semi-relativistic equation.
Obtained series solutions for the differential equation.
Provided insights into the dynamics of heavy quark systems.
Abstract
We approximate the two-body spinless Salpeter equation with the one which is valid in heavy quarks limit. We consider the resulting semi-relativistic equation in a time-dependent formulation. We use the Lewis- Riesenfeld dynamical invariant method and series solution to obtain the solutions of the differential equation. We have also done some calculations in order to derive the time evolution operator for the considered problem.
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Taxonomy
TopicsModel Reduction and Neural Networks · Numerical methods for differential equations