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J. Phys. A: Math. Gen. 32 No 39 (1 October 1999) 6891-6896
PII: S0305-4470(99)04438-8

Variational principle for critical parameters of quantum systems

A V Sergeev and S Kais
Purdue University, Department of Chemistry, 1393 Brown Building, West Lafayette, IN 47907, USA

Received 20 May 1999, in final form 27 July 1999

Abstract. The variational principle for eigenvalue problems with a nonidentity 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 nonlinear 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 subjected to a magnetic field are found using a product of two hydrogen-like basis sets.


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