Two-Dimensional Stationary Phase Approximation: Stationary Point at a Corner

Author(s):  
J. P. McClure ◽  
R. Wong





Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 493
Author(s):  
Jose M. Cerveró ◽  
Pilar G. Estévez

A review of the mathematical and physical aspects of the Ermakov systems is presented. The main properties of Lie algebra invariants are extensively used. The two and tridimensional Ermakov systems are fully analyzed and the correspondent invariants found. Then, we go over quantization with special emphasis in the two dimensional case. An application to Nonlinear Optics is hereby developed. We also treat the so-called “one dimensional” case, which is easily solved in the classical case but offers special interest in the quantum realm, where one can find exactly the Feynman propagator. We finish with the stationary phase approximation which contains also some interesting features when compared with the exact solution. Some prospects for future research are also discussed.





1975 ◽  
Vol 12 (7) ◽  
pp. 2031-2036 ◽  
Author(s):  
Hector Moreno ◽  
H. M. Fried


2021 ◽  
Vol 188 (10) ◽  
Author(s):  
Tiantian Si ◽  
Xiaofeng Lu ◽  
Haixia Zhang ◽  
Xiaojing Liang ◽  
Shuai Wang ◽  
...  




1997 ◽  
Vol 56 (12) ◽  
pp. 7589-7597 ◽  
Author(s):  
Ludger Wirtz ◽  
Jian-Zhi Tang ◽  
Joachim Burgdörfer


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