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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