QUANTIZATION OF SECOND-ORDER CONSTRAINED LAGRANGIAN SYSTEMS USING THE WKB APPROXIMATION

2005 ◽  
Vol 02 (03) ◽  
pp. 485-504 ◽  
Author(s):  
EQAB M. RABEI ◽  
EYAD H. HASSAN ◽  
HUMAM B. GHASSIB ◽  
S. MUSLIH
Keyword(s):  
Wave Function ◽  
General Theory ◽  
Semiclassical Limit ◽  
Second Order ◽  
Constrained Systems ◽  
Wkb Approximation ◽  
Lagrangian Systems

A general theory is given for quantizing both constrained and unconstrained systems with second-order Lagrangian, using the WKB approximation. In constrained systems, the constraints become conditions on the wave function to be satisfied in the semiclassical limit. This is illustrated with two examples.

Quantization of fractional singular Lagrangian systems using WKB approximation

2018 ◽  
Vol 33 (36) ◽  
pp. 1850222 ◽  
Author(s):  
Eqab M. Rabei ◽  
Mohammed Al Horani
Keyword(s):  
Wave Function ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Singular Systems ◽  
Equations Of Motion ◽  
Singular System ◽  
Wkb Approximation ◽  
Lagrangian System ◽  
Lagrangian Systems ◽  
Action Integral

In this paper, the fractional singular Lagrangian system is studied. The Hamilton–Jacobi treatment is developed to be applicable for fractional singular Lagrangian system. The equations of motion are obtained for the fractional singular systems and the Hamilton–Jacobi partial differential equations are obtained and solved to determine the action integral. Then the wave function for fractional singular system is obtained. Besides, to demonstrate this theory, the fractional Christ-Lee model is discussed and quantized using the WKB approximation.

scholarly journals Perturbations of nonlinear autonomous oscillators

1994 ◽  
Vol 35 (4) ◽  
pp. 445-468 ◽  
Author(s):  
P. B. Chapman
Keyword(s):  
General Theory ◽  
Fourier Coefficients ◽  
Multiple Scales ◽  
Second Order ◽  
Multiple Scales Method ◽  
Suitable Parameter ◽  
Non Linear

AbstractA general theory is given for autonomous perturbations of non-linear autonomous second order oscillators. It is found using a multiple scales method. A central part of it requires computation of Fourier coefficients for representation of the underlying oscillations, and these coefficients are found as convergent expansions in a suitable parameter.

General theory of second order isoparametric elements

1987 ◽  
pp. 91-103
Author(s):  
Jean-Claude Sabonnadière ◽  
Jean-Louis Coulomb
Keyword(s):  
General Theory ◽  
Second Order ◽  
Isoparametric Elements

Robust holography of the temporal wave function via second-order interference

2019 ◽  
Vol 100 (4) ◽  
Author(s):  
Yao-Kun Xu ◽  
Shi-Hai Sun ◽  
Wei-Tao Liu ◽  
Ji-Ying Liu ◽  
Ping-Xing Chen
Keyword(s):  
Wave Function ◽  
Second Order

The effects of ground state correlations in 16O on the muonuclear sum rule

1982 ◽  
Vol 60 (3) ◽  
pp. 321-328 ◽  
Author(s):  
D. Duplain ◽  
B. Goulard
Keyword(s):  
Wave Function ◽  
Cluster Expansion ◽  
Ground State ◽  
Neutrino Energy ◽  
Tensor Component ◽  
Second Order ◽  
Muon Capture ◽  
Total Rate ◽  
Sum Rule ◽  
The Mean

The total rate of muon capture by 16O is calculated using the linked cluster expansion to introduce ground state correlations. All diagrams up to the second order in the number of hole-lines are included. [Formula: see text] is reduced by some 15% and is shown to behave like σ−1,. [Formula: see text] and [Formula: see text] are strongly increased by about 30%. This enhancement is related to that part of the defect wave function which arises directly from the tensor component of the N–N potential. It is suggested that, for those transitions that are induced by spin operators, the mean neutrino energy may be smaller than usually thought.

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