A NEW APPROACH TO THE STUDY OF NOETHER INVARIANTS AND SYMMETRY ALGEBRAS

In this paper, the driven generalized time-dependent harmonic oscillator (DGTHO) is studied by making use of the new concept of quantum basic invariants. The connection between the quantum basic invariants and classical Noether's theorem is discussed. The classical basic invariants as well as the general form of classical invariants for the system are found. From these, we get the five Noether invariants and the set of corresponding infinitesimal generators {G(k)}, hence, generalizing the work of G. Profilo and G. Soliani. Also, for the system, we calculate the current algebra which, as the central extension of the {G(k)} algebra, should be regarded as the dynamical symmetry algebra for the system and is therefore more important than the {G(k)} algebra. Finally, we demonstrate the existence of a kind of converse of Noether's theorem.