A Practical Method for the Solution of Certain Problems in Quantum Mechanics by Successive Removal of Terms from the Hamiltonian by Contact Transformations of the Dynamical Variables Part II. Power Series in a Coordinate and Its Conjugate Momentum. The Anharmonic Oscillator by Perturbation Theory

1942 ◽  
Vol 10 (8) ◽  
pp. 538-545 ◽  
Author(s):  
L. H. Thomas
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Power Series ◽  
Anharmonic Oscillator ◽  
Practical Method ◽  
Conjugate Momentum ◽  
Contact Transformations ◽  
Successive Removal

Quantum mechanics of the isotropic three-dimensional anharmonic oscillator

1964 ◽  
Vol 60 (2) ◽  
pp. 273-278 ◽  
Author(s):  
I. J. Zucker
Keyword(s):  
Quantum Mechanics ◽  
Power Series ◽  
Potential Function ◽  
Anharmonic Oscillator ◽  
Three Dimensional ◽  
Spherically Symmetric ◽  
Symmetric Potential ◽  
Eigen Values

AbstractA method of determining numerically to any degree of accuracy the eigen-values of Hamiltonians in the form of power series is presented. The case of a spherically symmetric potential function of the form V = ar2 + br4 + cr6 is treated in detail.

A general iterative time-independent perturbation theory

1985 ◽  
Vol 63 (9) ◽  
pp. 1157-1161 ◽  
Author(s):  
F. Castaño ◽  
L. Laín ◽  
M. N. Sanchez ◽  
A. Torre
Keyword(s):  
Perturbation Theory ◽  
Power Series ◽  
Iterative Method ◽  
Perturbation Methods ◽  
Lennard Jones ◽  
Insight Into ◽  
Considerable Insight

An iterative method for time-independent perturbation theory is presented. Lennard-Jones–Brillouin–Wigner (LBW) and Rayleigh–Schrödinger (RS) power series are shown to be particular cases of the iteration and the combined expansion–iteration. Improvements in convergence of the power series are suggested and analyzed.The iterative method gives considerable insight into the nature and relative convergence of the currently used time-independent perturbation methods.

scholarly journals New perturbation theory for the nonstationary anharmonic oscillator

1997 ◽  
Vol 30 (21) ◽  
pp. 7413-7425
Author(s):  
Alexander V Bogdanov ◽  
Ashot S Gevorkyan
Keyword(s):  
Perturbation Theory ◽  
Anharmonic Oscillator ◽  
New Perturbation

Quantum mechanics of the anharmonic oscillator

1973 ◽  
Vol 14 (2) ◽  
pp. 219-227 ◽  
Author(s):  
Francis R. Halpern
Keyword(s):  
Quantum Mechanics ◽  
Anharmonic Oscillator

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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