Practical recursive solution of degenerate Rayleigh-Schrödinger perturbation theory and application to high-order calculations of the Zeeman effect in hydrogen

1981 ◽  
Vol 23 (4) ◽  
pp. 1645-1654 ◽  
Author(s):  
Harris J. Silverstone ◽  
Richard K. Moats
Keyword(s):  
Perturbation Theory ◽  
Zeeman Effect ◽  
High Order ◽  
Recursive Solution ◽  
Schrödinger Perturbation

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.

THE CALCULATION OF VARIOUS QUANTITIES WITHIN PERTURBATION THEORY AT THE 3- AND 4-LOOP ORDER

1995 ◽  
Vol 06 (04) ◽  
pp. 513-518 ◽  
Author(s):  
T. VAN RITBERGEN ◽  
J.A.M. VERMASEREN ◽  
S.A. LARIN ◽  
P. NOGUEIRA
Keyword(s):  
Perturbation Theory ◽  
Quark Mass ◽  
Decay Rates ◽  
High Order ◽  
Loop Order ◽  
Perturbative Calculations ◽  
Methods And Techniques ◽  
Mass Expansion

We discuss methods and techniques that were recently used in the following high order perturbative calculations: the large quark mass expansion of the decay rates Z0→ hadrons and τ→ν+ hadrons and the calculation of various quantities for deep inelastic lepton hadron scattering. Progress on the automatization of some general procedures is discussed.

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