𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Upper and lower bounds to critical values of the Hartree operator

✍ Scribed by R. Behling; A. Bongers; T. Küpper

Publisher
John Wiley and Sons
Year
1976
Tongue
English
Weight
393 KB
Volume
10
Category
Article
ISSN
0020-7608

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Upper and lower bounds for the minimal critical energy E of the Hartree operator for helium are calculated. We show that a Ritz analogous procedure for the calculation of the upper bounds converges to the exact value. The lower bound to E yields that the ground state E~H~ of the helium atom is strictly lower than 2__E__.

📜 SIMILAR VOLUMES

Existence and bounds for critical energi
Existence and bounds for critical energies of the hartree operator
✍ N. Bazley; R. Seydel 📂 Article 📅 1974 🏛 Elsevier Science 🌐 English ⚖ 280 KB

A method is presented for proving the existence and calculating lower bounds for critiml energies of the Hartrec equation for rhe helium atom. Our idea is to introduce an "energy" scalar product and use it to approximate the fourth order term in the potential by n smaller second order term. Rigorous

Upper and lower bounds to the Schrödinge
Upper and lower bounds to the Schrödinger equation eigenvalues
✍ Francisco M. Fernández 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 230 KB

## Abstract A method is presented for obtaining rapidly convergent upper and lower bounds to the eigenvalues of the Schrödinger equation for one‐dimensional and central‐field models. The logarithmic derivative of the wave function is written as a Padé approximant and the bounds are obtained by simp

Lower and upper bounds for the perturbat
Lower and upper bounds for the perturbation of linear operators equations
✍ Jiu Ding 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 202 KB

Let X and Y be Banach spaces, and let T : X -Y be a bounded linear operator with closed range. In this paper, we give optimal lower and upper bounds for the perturbation of consistent operator equations Tz = 1/, and more general least-squares problems in Hilbert spaces.