Degenerate Perturbation Theory in Quantum Mechanics

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.

Citing Article(s):

1. Progress of Theoretical Physics Vol. 71 No. 6 (1984) pp. 1221-1238

   General Structure of Effective Interaction in Degenerate Perturbation Theory Kenji Suzuki and Ryoji Okamoto

2. Progress of Theoretical Physics Vol. 72 No. 3 (1984) pp. 534-548

   Perturbation Theory for Quasidegenerate System in Quantum Mechanics Kenji Suzuki and Ryoji Okamoto

3. Progress of Theoretical Physics Vol. 75 No. 6 (1986) pp. 1388-1404

   Unitary-Model-Operator Approach to Nuclear Many-Body Problem. I Kenji Suzuki and Ryoji Okamoto

4. Progress of Theoretical Physics Vol. 76 No. 1 (1986) pp. 127-142

   Unitary-Model-Operator Approach to Nuclear Many-Body Problem. II Kenji Suzuki and Ryoji Okamoto

5. Progress of Theoretical Physics Vol. 79 No. 2 (1988) pp. 330-342

   Theory of Many-Fermion System on Unitary-Transformation Method Kenji Suzuki

6. Progress of Theoretical Physics Vol. 92 No. 6 (1994) pp. 1045-1080

   Effective Interaction Theory and Unitary-Model-Operator Approach to Nuclear Saturation Problem Kenji Suzuki and Ryoji Okamoto

7. Progress of Theoretical Physics Vol. 93 No. 5 (1995) pp. 905-917

   Effective Operators in Time-Independent Approach Kenji Suzuki and Ryoji Okamoto

© Copyright (c) 1983 Progress of Theoretical Physics 1983