  We perform a short review of the history of quantum mechanics, with a focus
on the historical problems with describing ionization theoretically in the
context of quantum mechanics. The essentials of the theory of resonances are
presented. The exterior complex scaling method for obtaining resonance
parameters within the context of the Schrodinger equation is detailed. We
explain how this is implemented for a numerical solution using a finite element
method for the scaled variable. Results for the resonance parameters of a
one-dimensional hydrogen model in an external direct current (DC) electric
field are presented as proof of the independence of the theory from the scaling
angle. We apply the theory to the real hydrogen atom in a DC field and present
results which agree with literature values. The resonance parameters for singly
ionized helium are also presented. Using a model potential energy for the water
molecule, we solve for the energy eigenvalues. We then solve for the resonance
parameters of the water molecule in a DC field and compare to literature
results. Our widths for the valence orbital are shown to agree well with the
so-called "coupled-cluster singles and doubles with perturbative triples
excitations" method.
