Nonperturbative corrections to bound states of the quasipotential equation by Padé approximants

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Abstract
A nonperturbative approach to the relativistic bound-state problem is tested in a simplified version of quantum electrodynamics. The approach used is based on applying Padé approximants to a perturbation series of quasipotentials derived from an inhomogeneous quasipotential equation. The resultant nonperturbative form of the quasipotential is used in solving the homogeneous quasipotential equation (relativistic Schrödinger equation). The size of the nonperturbative results of the Lamb shift is compared with that of the perturbative results. As with real quantum electrodynamics for point particles, this simplified model we use to test our approach gives complex energies if the coupling constant is larger than some critical value. The change of this critical value of the coupling constant which results from using a nonperturbative form of the potential is computed.

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