Pseudo-potential approach including relativistic effects

1978 ◽  
Vol 11 (2) ◽  
pp. 217-233 ◽  
Author(s):  
P Hafner ◽  
W H E Schwarz
Keyword(s):  
Relativistic Effects ◽  
Potential Approach ◽  
Pseudo Potential

scholarly journals Relativistic Ermakov-Milne-Pinney Systems and First Integrals

2021 ◽  
Author(s):  
Fernando Haas
Keyword(s):  
Physical Interpretation ◽  
Relativistic Effects ◽  
First Integral ◽  
First Integrals ◽  
Nonlinear Superposition ◽  
Relativistic Limit ◽  
Guiding Principle ◽  
Relativistic Analog ◽  
Relativistic Extension ◽  
Pseudo Potential

The Eliezer and Gray physical interpretation of the Ermakov-Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov-Milne-Pinney equation and associated first integral. The special relativistic extension of the Ray-Reid system and invariant is obtained. General properties of the relativistic Ermakov-Milne-Pinney are analyzed. The conservative case of the relativistic Ermakov-Milne-Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered as well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov-Milne-Pinney equation has additional nonlinearities, due to the relativistic effects.

Speed and Shape of Electrostatic Waves in Dust-Ion Plasma

2006 ◽  
Vol 61 (12) ◽  
pp. 661-666 ◽  
Author(s):  
Prasanta Chatterjee ◽  
Bholanath Sen
Keyword(s):  
Solitary Waves ◽  
Soliton Solution ◽  
Acoustic Waves ◽  
Critical Value ◽  
Magnetized Plasma ◽  
Electrostatic Waves ◽  
Potential Approach ◽  
Ion Plasma ◽  
Dust Acoustic ◽  
Pseudo Potential

Nonlinear dust acoustic waves are studied in a magnetized plasma. Quasineutrality is considered. The existence of a soliton solution is determined by a pseudo-potential approach. Sagdeev’s potential is obtained in terms of U(= αudx +γudz), the component of the dust-ion velocity in the direction of the propagation of the wave. It is shown that there exists a critical value of U, beyond which the solitary waves cease to exist.

Theory of impurity and defect induced instabilities

1992 ◽  
Vol 341 (1661) ◽  
pp. 247-253
Keyword(s):  
Ab Initio ◽  
Tight Binding ◽  
Current Status ◽  
Native Defects ◽  
Potential Approach ◽  
Interstitial Impurities ◽  
Interstitial Defect ◽  
Defect Centres ◽  
Pseudo Potential ◽  
Modelling Process

A brief review of the current status of our work on substitutional and interstitial impurities and native defects in GaAs and of the modelling process used in the calculations is given. The combined empirical tight-binding and ab initio pseudo-potential approach utilized in these studies allows for efficient testing of a large number of structural possibilities and the identification of the most relevant ones. Applications of the method and new results for EL2, DX, and self-interstitial defect centres in GaAs are discussed.

Pseudo potential approach to a theory of positron alkali atom bound states

1971 ◽  
Vol 34 (5) ◽  
pp. 297-298 ◽  
Author(s):  
P. Cavaliere ◽  
G. Ferrante ◽  
P. Manno
Keyword(s):  
Bound States ◽  
Alkali Atom ◽  
Potential Approach ◽  
Pseudo Potential
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