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Perturbation theory in the path‐integral representation and its application to some simple quantum systems
Author(s) -
Perlin Y. U. E.,
Gifeisman S. H. N.,
Van Quyet Pham
Publication year - 1977
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.560120202
Subject(s) - path integral formulation , feynman diagram , formalism (music) , quantum , physics , quantum mechanics , coulomb , perturbation theory (quantum mechanics) , perturbation (astronomy) , ground state , electron , art , musical , visual arts
In the framework of the path‐integral formalism of nonrelativistic quantum theory the perturbation method is developed. This is based on the cumulative expansion of the partition function in powers of the difference between the classical actions of the exact and trial system. The trial system is constructed by replacing the Coulomb interactions by elastic ones, with parameters defined by Feynman's variational principle. The second order corrections to the ground‐state energy of the hydrogen and helium atoms, the hydrogen molecule, and molecular ion have been evaluated. The results have been found to coincide with the actual values with an accuracy of 4–6%, whereas the corresponding error of the variational solution is of the order of 15–20%.