scholarly journals Perturbation Theory of Relativistic Eigenvalue Problem

1953 ◽  
Vol 10 (1) ◽  
pp. 108-109
Author(s):  
Nobumichi Mugibayashi ◽  
Mikio Namiki
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem

scholarly journals Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem

2003 ◽  
Vol 2003 (9) ◽  
pp. 459-485
Author(s):  
Brian J. McCartin
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Symmetric Matrix ◽  
Comprehensive Treatment ◽  
Matrix Eigenvalue Problem ◽  
Degenerate Problem ◽  
Matrix Eigenvalue ◽  
Penrose Pseudoinverse ◽  
Schrödinger Perturbation

A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix-theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher-order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example.

Comments on Rayleigh’s Quotient and Perturbation Theory for the Eigenvalue Problem

1988 ◽  
Vol 55 (4) ◽  
pp. 986-988 ◽  
Author(s):  
Christophe Pierre
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Rayleigh’S Quotient

The connection between Rayleigh’s quotient and perturbation theory for the eigenvalue problem is studied. Equivalence of these techniques is proven under certain conditions.

scholarly journals Closed form bound-state perturbation theory

1980 ◽  
Vol 3 (2) ◽  
pp. 351-368 ◽  
Author(s):  
Ollie J. Rose ◽  
Carl G. Adler
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Closed Form ◽  
Bound States ◽  
Integral Form ◽  
Approximate Solutions ◽  
Perturbation Parameter ◽  
Bound State ◽  
The Given ◽  
Natural Way

The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.

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