Combination of the successive perturbation method with other common methods

1987 ◽  
Vol 65 (5) ◽  
pp. 462-463 ◽  
Author(s):  
V. A. Popescu ◽  
I. M. Popescu
Keyword(s):  
Hydrogen Atom ◽  
Perturbation Method ◽  
Perturbation Series ◽  
Radius Of Convergence ◽  
Fundamental State

For the hydrogen atom in the fundamental state perturbed by βr−1, it is shown how the successive perturbation method can be combined with the method in which some fraction of a nonperturbed term (in the Hamiltonian) is included in the perturbation. Thus, the radius of convergence of the perturbation series is increased.

The Validity of Perturbation Series with Zero Radius of Convergence

1966 ◽  
Vol 7 (11) ◽  
pp. 1900-1902 ◽  
Author(s):  
George A. Baker ◽  
Roy Chisholm
Keyword(s):  
Perturbation Series ◽  
Radius Of Convergence ◽  
Zero Radius

EXACT SOLITARY-WAVE SOLUTIONS FOR THE NONLINEAR DISPERSIVE K(2,2,1) and K(3,3,1) EQUATIONS BY THE HOMOTOPY PERTURBATION METHOD

2009 ◽  
Vol 23 (30) ◽  
pp. 3667-3675 ◽  
Author(s):  
AHMET YILDIRIM
Keyword(s):  
Exact Solution ◽  
Solitary Wave ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Convergent Series ◽  
Perturbation Series ◽  
Solitary Wave Solutions ◽  
Homotopy Perturbation ◽  
Wave Solutions ◽  
Explicit Exact Solution

We implemented homotopy perturbation method for approximating the solution to the nonlinear dispersive K(m,n,1) type equations. By using this scheme, the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. To illustrate the application of this method, numerical results are derived by using the calculated components of the homotopy perturbation series.

Summation of the perturbation series for the energy levels of a hydrogen atom in a magnetic field

1983 ◽  
Vol 102 (4) ◽  
pp. 344-353 ◽  
Author(s):  
Gustavo A. Arteca ◽  
Francisco M. Fernandez ◽  
Eduardo A. Castro
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Energy Levels ◽  
Perturbation Series

O(4)-Symmetrie und Stark-Effekt des H-Atoms / O(4)-Symmetry and Stark-Effect of the H-Atom

1976 ◽  
Vol 31 (6) ◽  
pp. 517-523 ◽  
Author(s):  
H. G. Becker ◽  
K. Bleuler
Keyword(s):  
Perturbation Theory ◽  
Hydrogen Atom ◽  
Perturbation Method ◽  
Stark Effect ◽  
Second Order ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Quantum Mechanical ◽  
Third Order

Using the advantages of the O (4)-symmetry the second order Stark-effect of the hydrogen atom is calculated by the Dalgarno-Lewis perturbation method in a purely algebraic manner. The Starkeffect provides the first quantum mechanical example in which the Dalgarno-Lewis equation relevant for second and third order perturbation theory of the whole spectrum can be exactly solved

The successive perturbation method in the various orders of perturbation

1990 ◽  
Vol 68 (12) ◽  
pp. 1476-1478
Author(s):  
V. A. Popescu ◽  
I. M. Popescu ◽  
M. Jitaru
Keyword(s):  
Perturbation Method ◽  
Interaction Parameter ◽  
Complex Plane ◽  
Energy Levels ◽  
Perturbation Expansion ◽  
Radius Of Convergence ◽  
Variational Functional ◽  
Functional Methods

We consider the case where the radius of convergence of the perturbation expansion can be related to a "crossing" of two energy levels in the complex plane of the interaction parameter. This case is suitable for the comparison of the performance of the successive perturbation method with those of the Padé, Borel–Padé, and the variational functional methods.

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