Application of the variational principle to perturbation theory

1994 ◽  
Vol 62 (4) ◽  
pp. 379-380 ◽  
Author(s):  
V. Hushwater
Keyword(s):  
Perturbation Theory ◽  
Variational Principle

The use of the variational principle in molecular perturbation theory

1985 ◽  
Vol 82 (9) ◽  
pp. 4276-4282 ◽  
Author(s):  
Saul Goldman ◽  
Bijoy Kumar
Keyword(s):  
Perturbation Theory ◽  
Variational Principle

Variational methods and applications to water waves

1967 ◽  
Vol 299 (1456) ◽  
pp. 6-25 ◽  
Keyword(s):  
Perturbation Theory ◽  
Variational Principle ◽  
Variational Methods ◽  
Water Waves ◽  
Important Application ◽  
Lagrangian Function ◽  
Interaction Theory ◽  
Dispersive Waves ◽  
Linear Interaction ◽  
Long Wave

This paper reviews various uses of variational methods in the theory of nonlinear dispersive waves, with details presented for water waves. The appropriate variational principle for water waves is discussed first, and used to derive the long-wave approximations of Boussinesq and Korteweg & de Vries. The resonant near-linear interaction theory is presented briefly in terms of the Lagrangian function of the variational principle. Then the author’s theory of slowly varying wavetrains and its application to Stokes’s waves are reviewed. Luke’s perturbation theory for slowly varying wavetrains is also given. Finally, it is shown how more general dispersive relations can be formulated by means of integro-differential equations; an important application of this, developed with some success, is towards resolving longstanding difficulties in understanding the breaking of water waves.

Polaron Effect on the D- Center at the InP(GaP) Heterointerface in a Magnetic Field

2012 ◽  
Vol 430-432 ◽  
pp. 16-19
Author(s):  
Xiao Yan Zhang ◽  
Guo Liang Fan
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Variational Principle ◽  
Triplet State ◽  
Numerical Results ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Polaron Effect ◽  
Spin Triplet ◽  
Second Order Perturbation Theory

Effect of polaron on the spin triplet state (p-like) of the center is discussed by means of variational principle and second-order perturbation theory. Numerical results are produced for heterostructures of InP(GaP) in a magnetic field. We find that the polaron correction is very important. The contribution of the polaron is not negligible.

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