COMPLETE SYMMETRY GROUP OF THE ONE-DIMENSIONAL TIME-DEPENDENT HARMONIC-OSCILLATOR

The five invariants for the time-dependent one-dimensional harmonic oscillator Hamiltonian are constructed. Using the linear transformation to the time-dependent oscillator Hamiltonian, the five invariants for the latter are obtained. The differential operators which generate the dynamical symmetry of this Hamiltonian have the same commutator relations as these of the time-independent problem. An additional three operators are obtained using the method of extended Lie groups and have the same properties as those for the time-independent problem. Thus the complete dynamical symmetry of the time-dependent problem is the eight-parameter Lie group SL(3,R). © 1980 American Institute of Physics.