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Second Order Invariants for Two Dimensional Classical Dynamical Systems
Author(s) -
Kaushal R. S.,
Parashar D.,
Mishra S. C.
Publication year - 1994
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190420803
Subject(s) - harmonic oscillator , integrable system , quadratic equation , dynamical systems theory , class (philosophy) , physics , quantum , classical mechanics , coherent states , theoretical physics , mathematics , pure mathematics , algebra over a field , quantum mechanics , mathematical physics , computer science , geometry , artificial intelligence
A general method is used to construct explicitly the quadratic invariants for two dimensional classical dynamical systems. The solutions of the “potential” equations are considered for both time dependent (TD) and time independent (TID) systems dealing mainly with the noncentral potentials. While several interesting integrable TID systems are found, which may have applications in solid state physics and molecular chemistry, an explicit construction of the invariants for a large class of TD systems is carried out which may again be useful in quantum optics and astronomy. In particular, the problem of noncentral TD harmonic oscillator in its varied form is dealt with in some details.