Hylleraas Phys

Hylleraas E A 1963 Reminisoenoes from early quantum meohanios of two-eleotron atoms Rev. Mod. Phys. 35 421-31... 

This characteristic is commonly referred to as the bracketing theorem (E. A. Hylleraas and B. Undheim, Z. Phys. 759 (1930) J. K. E. MacDonald, Phys. Rev. 43, 830 (1933)). These are strong attributes of the variational methods, as is the long and rich history of developments of analytical and computational tools for efficiently implementing such methods (see the discussions of the CI and MCSCF methods in MTC and ACP). 

Green, L. C., Mulder, M. M., Milner, P. C., Lewis, M. N., Woll, J. W., Jr., Kolchin, E. K., and Mace, D., Phys. Rev. 96, 319, (iii) Analysis of the three parameter wave function of Hylleraas for the He I ground state in terms of central field wave-functions/ Configurational interaction. 

Shull, H., and Lowdin, P.-O., J. Chew. Phys. 23, 1362, "Role of the continuum in superposition of configurations." Criticism of Taylor and Parr (1952). Emphasis of the work by Hylleraas (1928). 

Hylleraas, E. A., and Midtdal, J., Phys. Rev. 103, 829, Ground state energy of two-electron atoms. ... 

Schwartz, H. M., Phys. Rev. 103, 110, "Ground state solution of the non-relativistic equation for He." More rapid convergence in the Ritz variational method by inclusion of half-integral powers in the Hylleraas function. 

E. A. Hylleraas, Z Phys. 65 (1930), 209 note 6, p. 279. Note that if(2) can alternatively be expressed as an infinite expansion in the unperturbed eigenfunctions but the Hylleraas variation-perturbation expression (1.5d) is generally more useful for practical numerical applications. 

Hylleraas, E.A. Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium. Z. Phys. 1929, 54, 347-66. 

Bhatia, A.K., Temkin, A., Drachman, R.J. and Eiserike, H. (1971). Generalized Hylleraas calculation of positron-hydrogen scattering. Phys. Rev. A 3 1328-1335. 

A.K. Bhatia, A. Temkin, J.F. Perkins, Hylleraas variational calculation of auto-ionization states, Phys. Rev. 153 (1967) 177. 

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