# Variational principle for critical parameters
of quantum systems

## A. V. Sergeev and Sabre Kais

Variational principle for eigenvalue problems with a non-identity weight operator
is used to establish upper or lower bounds on critical parameters of quantum
systems. Three problems from atomic physics are considered as examples. Critical
screening parameters for the exponentially screened Coulomb potential are
found using a trial function with one non-linear variational parameter. The
critical charge for the helium isoelectronic series is found using a Hylleraas-type
trial function. Finally, critical charges for the same system subject to a
magnetic field are found using a product of two hydrogen-like basis sets.

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