QUANTUM BASIC INVARIANTS AND CLASSICAL NOETHER THEOREM

Taking the generalized time-dependent harmonic oscillator (GTHO) and s ingular time-dependent harmonic oscillator (STHO) as illustrative exam ples, we discuss the connection between the quantum basic invariants a nd classical Noether's theorem and, for the system, find: (1) The clas sical basic invariants and general form of classical invariants. (2) T he current algebra and corresponding operator algebra. (3) A kind of c onverse of the Noether's theorem. (4) The connection between the so-ca lled symmetry algebra ({G(k)} algebra) and the classical current algeb ra through the operator algebra.