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Variational solutions of a first‐order perturbation equation
Author(s) -
Hamano Hidekazu
Publication year - 1982
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.560210308
Subject(s) - harmonic oscillator , hydrogen atom , perturbation (astronomy) , perturbation theory (quantum mechanics) , dipole , variational method , poincaré–lindstedt method , physics , quantum mechanics , mathematical analysis , mathematics , classical mechanics , quantum electrodynamics , group (periodic table)
The variation‐perturbation method for solving a first‐order equation of Rayleigh‐Schrödinger perturbation theory is presented. The method consists of the combination of variational procedures and successive approximations. The recurrence formulas generate successively the higher‐order approximations of the variational solutions. It is possible to obtain the almost exact solution within a few steps. The method is applied to the calculations of the polarizabilities of a one‐dimensional harmonic oscillator and of the hydrogen atom, and the dipole‐dipole interaction energy of two hydrogen atoms.