Formalisms of Quantization in High Intensity Fields: Quantum Mechanics Meets Classical Electrodynamics

We studied the possible formalisms used in both Quantum Electrodynamics and Classical Electrodynamics, that might be sharing same methodologies that turns out to be in quantization of the fields, despite of the fact that the field is an infinite wave. In one side we used the Volkov solutions while in the classical counterpart we used the formalism of Hartemann-Kerman. The obtained simulations would demonstrate that quantum and classical methodologies are based on the same mathematical basis that use the integer-order Bessel's functions.