Abstract
A general approximation method is developed to find the state of a system composed of a low-energy free electron and hydrogen atom in an intense electromagnetic field. The electron wave function includes two parts: One, of infinite extension, represents a free-electron state in an electromagnetic field; the other, localized on the atom, is a bound pseudostate. This method complements and takes its place among other known methods used for weak electromagnetic fields or high-energy electrons. It can be applied to interaction scalar potentials which decrease faster than $\frac{1}{r}$.
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