Integrals for lower bounds to the exact energy

2021/07/07 by Robbie T. Ireland, Robbie Thomson Ireland, Ireland, Robbie Thomson
Computer Science · Mathematics · Medicine · Physics and Astronomy · #Applied mathematics #Calculus (dental) #Energy (signal processing) #FOS: Physical sciences #Mathematics #Matrix Theory and Algorithms #Medicine #Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Statistics #quant-ph

paper · pdf · doi:10.48550/arxiv.2107.03469

arxiv created 2021/07/07 · openalex publication_date 2021/07/07 · arxiv updated 2021/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known solutions could be found in the literature are derived for an explicitly correlated Gaussian (ECG) basis set. Analytical Solutions are determined for two-electron, mono-nuclear systems, in addition to a one-dimensional integral expression which has use in polyatomic calculations. The newly derived integral expressions have been implemented in the integral library of the QUANTEN computer program.

Citations

• Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik.
• Numerische Berechnung der 2S-Terme von Ortho- und Par-Helium
• Zur Quantentheorie der Molekeln
• Review of Particle Physics

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