Abstract
Coupled integral equations for bound states of two spin-0 bosons are derived variationally from scalar quantum electrodynamics, using an ansatz which incorporates the transverse photon degrees of freedom of the electromagnetic field. The equations are decoupled approximately and then solved perturbatively as well as numerically. A perturbative eigenenergy formula for particles of arbitrary masses, including all the corrections of order ${\mathrm{\ensuremath{\alpha}}}^{4}$, is obtained. A variational solution of the wave equation is used to determine eigenvalues and eigenfunctions at arbitrary coupling for the 1s and 2p states of the equal-mass and ${\mathit{m}}_{\mathit{K}}$/${\mathit{m}}_{\mathrm{\ensuremath{\pi}}}$ cases. Radial s-state excitations are calculated using the basis-state expansion method. In the limit where one particle becomes infinite our equation turns out to be the same as the weak-field limit of the Klein-Gordon-Coulomb equation.
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