Perturbation Theory in Closed Form for Heteronuclear Diatomic Molecules

1973 ◽  
Vol 8 (2) ◽  
pp. 612-620 ◽  
Author(s):  
I. I. Tugov
Keyword(s):  
Perturbation Theory ◽  
Closed Form ◽  
Diatomic Molecules

Investigations in Many-Body Perturbation Theory of Hyperfine Structure in Diatomic Molecules

1973 ◽  
Vol 7 (1) ◽  
pp. 51-59 ◽  
Author(s):  
James E. Rodgers ◽  
Taesul Lee ◽  
T. P. Das ◽  
Dennis Ikenberry
Keyword(s):  
Perturbation Theory ◽  
Hyperfine Structure ◽  
Diatomic Molecules ◽  
Many Body ◽  
Many Body Perturbation Theory

scholarly journals Quantum square-well with logarithmic central spike

2018 ◽  
Vol 33 (02) ◽  
pp. 1850009 ◽  
Author(s):  
Miloslav Znojil ◽  
Iveta Semorádová
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Closed Form ◽  
Wave Functions ◽  
Change Of Variables ◽  
State Dependent ◽  
Square Well ◽  
Strength Formula ◽  
Schrödinger Perturbation ◽  
Dependent Interaction

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

scholarly journals A full wave description for thin wire structures with TLST and perturbation theory

2018 ◽  
Vol 16 ◽  
pp. 123-133
Author(s):  
Fabian Ossevorth ◽  
Ralf T. Jacobs ◽  
Hans Georg Krauthäuser
Keyword(s):  
Perturbation Theory ◽  
Closed Form ◽  
Current Distribution ◽  
Perturbation Approach ◽  
Mixed Potential ◽  
Thin Wire ◽  
Method Of Moment ◽  
Initial Current ◽  
Full Wave ◽  
Good Agreement

Abstract. A full wave description of a thin wire structure, that includes mutual interactions and radiation, can be obtained in closed form with the so-called Transmission Line Super Theory or a refined variant of this method that utilises perturbation theory. In either procedure, a set of mixed potential integral equations is solved for the currents that propagate along a wire. With the perturbation approach, no iteration is required to approximate the initial current distribution on the wire. This procedure will be applied to solve multi-wire problems. The theory will be derived and computed results will be shown to be in good agreement with method of moment computations.

PERTURBATIVE SOLUTIONS OF QUANTUM MECHANICAL PROBLEMS BY SYMBOLIC COMPUTATION: A REVIEW

1990 ◽  
Vol 01 (01) ◽  
pp. 53-76 ◽  
Author(s):  
T. C. SCOTT ◽  
R. A. MOORE ◽  
G. J. FEE ◽  
M. B. MONAGAN ◽  
G. LABAHN ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Power Series ◽  
Closed Form ◽  
Symbolic Computation ◽  
Order Parameter ◽  
Perturbation Series ◽  
Basis Set ◽  
Quantum Mechanical ◽  
Infinite Basis ◽  
Degenerate Perturbation Theory

It is shown that Symbolic Computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The method presented herein solves for both the eigenfunctions and eigenenergies as power series in the order parameter where each coefficient of the perturbation series is obtained in closed form. The algorithms are expressed in the Maple symbolic computation system but can be implemented on other systems. This approach avoids the use of an infinite basis set and some of the complications of degenerate perturbation theory. It is general and can, in principle, be applied to many separable systems.

Investigations in Many-Body Perturbation Theory of Hyperfine Structure in Diatomic Molecules

1973 ◽  
Vol 7 (6) ◽  
pp. 2222-2222 ◽  
Author(s):  
James E. Rodgers ◽  
Taesul Lee ◽  
T. P. Das ◽  
D. Ikenberry
Keyword(s):  
Perturbation Theory ◽  
Hyperfine Structure ◽  
Diatomic Molecules ◽  
Many Body ◽  
Many Body Perturbation Theory
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