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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