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Title: How to spoil a good basis set for Rayleigh-Ritz calculations

For model quantum mechanical systems such as the harmonic oscillator and a particle in an impenetrable box, we consider the set of exact discrete spectrum functions and define the modified basis set by subtraction of the ground state wavefunction from all the other wavefunctions with some real weights. It is demonstrated that the modified set of functions is complete in the space of square integrable functions if and only if the series of the squared weights diverges. A similar, but nonequivalent criterion is derived for convergence of Rayleigh-Ritz ground state energy calculations to the exact ground state energy value with the basis set extension. Some numerical illustrations are provided which demonstrate a wide variety of possible situations for model systems.
Authors:
 [1] ;  [2]
  1. Laboratory of Molecular Structure and Quantum Mechanics, Department of Chemistry, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
  2. Chemistry Program, Centre College, Danville, Kentucky 40422 (United States)
Publication Date:
OSTI Identifier:
22218150
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 8; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BASES; CONVERGENCE; DATA; GROUND STATES; HARMONIC OSCILLATORS; INTEGRAL CALCULUS; QUANTUM MECHANICS; RITZ METHOD; SOCIO-ECONOMIC FACTORS; WAVE FUNCTIONS