Rayleigh-Schrodinger perturbation theory with a strong perturbation: the quadratic Zeeman effect in hydrogen

1984 ◽  
Vol 17 (15) ◽  
pp. 3049-3055 ◽  
Author(s):  
M Cohen ◽  
S Kais
Keyword(s):  
Perturbation Theory ◽  
Zeeman Effect ◽  
Schrödinger Perturbation ◽  
Quadratic Zeeman Effect

THE THEORY OF THE QUADRATIC ZEEMAN EFFECT

1970 ◽  
Vol 31 (C4) ◽  
pp. C4-71-C4-74 ◽  
Author(s):  
A. R. EDMONDS
Keyword(s):  
Zeeman Effect ◽  
Quadratic Zeeman Effect

Semiclassical mechanics of the quadratic Zeeman effect

1992 ◽  
Vol 45 (5) ◽  
pp. 3093-3103 ◽  
Author(s):  
Kristin D. Krantzman ◽  
John A. Milligan ◽  
David Farrelly
Keyword(s):  
Zeeman Effect ◽  
Semiclassical Mechanics ◽  
Quadratic Zeeman Effect

Applicability of the schrödinger perturbation theory to bound states

1964 ◽  
Vol 10 (1) ◽  
pp. 73 ◽  
Author(s):  
K. Hausmann ◽  
W. Macke ◽  
P. Ziesche
Keyword(s):  
Perturbation Theory ◽  
Bound States ◽  
Schrödinger Perturbation

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.

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