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, which investigate particle production in the presence of 
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. With this method the perturbative QED result for the
electron anomalous magnetic moment is reproduced with a good accuracy. 
We also discuss the extension of the method to other problems as well.