“…wherex andp are the position and momentum operators following the standard commutation relations. Aside from the simple harmonic oscillator, a large number of interesting systems arise from this Hamiltonian as the linear potential, 28,29 the driven harmonic oscillator, 30,31 Kanai-Caldirola Hamiltonians, [16][17][18][19][20][21] and time dependent harmonic oscillators, i.e., an oscillator with time-varying frequency. 21,32,33 The time evolution generated by the most general version of (1) has been studied by means of Lewis and Riesenfeld 34 invariants 35 and through linear invariants.…”