  Non-perturbative solutions to the quantum-field theory is a topic of current
and broad interest, especially for the heavy ion and laser physics communities,
since they investigate particle production in the presence of strong external
fields. We have solved a non-perturbative QED + external field problem of an
electron in a strong transverse confining potential using Hamiltonian
light-front quantum field theory in a basis function representation. The
invariant mass spectra and the anomalous magnetic moment of the lowest state
for this two-scale system are also evaluated. With this method the perturbative
QED results are also reproduced with a good accuracy. We also discuss the
extension of the method to other problems as well.
