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A variation principle for energy differences between states of two different Hamiltonians
Author(s) -
Marron Michael T.,
Weare Johan H.
Publication year - 1968
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560020512
Subject(s) - variation (astronomy) , wave function , simple (philosophy) , energy (signal processing) , physics , first principle , quantum mechanics , mathematical physics , atomic physics , density functional theory , philosophy , epistemology , astrophysics
A modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ℋ] = 〈 X 0 | ℋ x – W x | X 1 〉 – 〈 Y 0 |ℋ y – W y | y 1 〉 + 〈 X 0 | Δ ℋ| Y 0 〉 · 〈 X 0 | Y 0 〉 −1 . Δ ℋ = ℋ y – ℋ x , | X 0 〉 and | Y 0 〉 are the wave functions for the X and Y states and | X 1 〉 and | Y 1 〉 are functions defined in the text. The principle is applied to a few simple examples.
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