Alexei Sergeev and Sabre Kais
Purdue University, Department of Chemistry
West Lafayette, IN 47906
Non-traditional applications of variational methods were proposed both for critical parameters (when the energy crosses the ionization threshold) and for the energy below and above ionization threshold.
If the critical parameter enters the Schrodinger equation linearly, then the equation for critical parameters can be considered as a generalized eigenvalue equation with a non-trivial weight operator. Consider, for example, a two-electron atom
H = p12/2 + p22/2 - Z/r1 - Z/r2 + 1/r12
with a charge Z treated as a continuous parameter . . .
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