scholarly journals Degenerate Perturbation Theory in Quantum Mechanics

1984 ◽  
Vol 71 (3) ◽  
pp. 670-670 ◽  
Author(s):  
K. Suzuki ◽  
R. Okamoto
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Degenerate Perturbation Theory

scholarly journals Time-independent perturbation theory with Lagrange multipliers

2021 ◽  
Author(s):  
Chaehyun Yu ◽  
Dong-Won Jung ◽  
U-Rae Kim ◽  
Jungil Lee
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Lagrange Multiplier ◽  
Lagrange Multipliers ◽  
Taylor Expansion ◽  
Constraint Equation ◽  
Characteristic Matrix ◽  
Straightforward Manner ◽  
New Formalism ◽  
Degenerate Perturbation Theory

AbstractWe derive the formulas for the energy and wavefunction of the time-independent Schrödinger equation with perturbation in a compact form. Unlike the conventional approaches based on Rayleigh–Schrödinger or Brillouin–Wigner perturbation theories, we employ a recently developed approach of matrix-valued Lagrange multipliers that regularizes an eigenproblem. The Lagrange-multiplier regularization makes the characteristic matrix for an eigenproblem invertible. After applying the constraint equation to recover the original equation, we find the solutions of the energy and wavefunction consistent with the conventional approaches. This formalism does not rely on an iterative way and the order-by-order corrections are easily obtained by taking the Taylor expansion. The Lagrange-multiplier regularization formalism for perturbation theory presented in this paper is completely new and can be extended to the degenerate perturbation theory in a straightforward manner. We expect that this new formalism is also pedagogically useful to give insights on the perturbation theory in quantum mechanics.

The application of analytical methods in degenerate perturbation theory

1974 ◽  
Vol 21 (3) ◽  
pp. 1229-1233
Author(s):  
A. G. Makhanek ◽  
V. S. Korol'kov ◽  
A. F. Fedorov
Keyword(s):  
Perturbation Theory ◽  
Analytical Methods ◽  
Degenerate Perturbation Theory

Successive approximation; perturbation theory in quantum mechanics

2021 ◽  
pp. 130-148
Author(s):  
Geoffrey Brooker
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Successive Approximation ◽  
Iterative Procedure ◽  
Approximation Problems

“Successive approximation; perturbation theory in quantum mechanics” introduces a toolbox for handling successive-approximation problems in any context. An iterative procedure is presented with examples. Newton's approximation is also an iterative procedure, but often other methods are better. Perturbation theory is presented, organized as an application of the toolbox.

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