Degenerate Perturbation Theory in Quantum Mechanics. Suzuki, K. & Okamoto, R. Progress of Theoretical Physics, 70(2):439–451, 1983.
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The relations are discussed among a number of different formulations of perturbation theory for an effective Hamiltonian of a general quantum system. Although the definitions and the formulations are apparently different, it is shown that the effective Hamiltonians, which have appeared in the history of time-independent approaches, can be written simply in a unified form. Expansion formulae are given explicitly for both the non-Hermitian and Hermitian effective Hamiltonians, and a discussion is given on a method for summing up the expansion series and obtaining a convergent result.
@article{Suzuki1983,
abstract = {The relations are discussed among a number of different formulations of perturbation theory for an effective Hamiltonian of a general quantum system. Although the definitions and the formulations are apparently different, it is shown that the effective Hamiltonians, which have appeared in the history of time-independent approaches, can be written simply in a unified form. Expansion formulae are given explicitly for both the non-Hermitian and Hermitian effective Hamiltonians, and a discussion is given on a method for summing up the expansion series and obtaining a convergent result.},
author = {Suzuki, K. and Okamoto, R.},
doi = {10.1143/ptp.70.439},
issn = {0033-068X},
journal = {Progress of Theoretical Physics},
number = {2},
pages = {439--451},
title = {{Degenerate Perturbation Theory in Quantum Mechanics}},
volume = {70},
year = {1983}
}

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