Department of Mathematics2024-11-1019980305-447010.1088/0305-4470/31/30/0142-s2.0-0032584456http://dx.doi.org/10.1088/0305-4470/31/30/014https://hdl.handle.net/20.500.14288/17626Quantum canonical transformations corresponding to time-dependent diffeomorphisms of the configuration space are studied. A special class of these transformations which correspond to time-dependent dilatations is used to identify a previously unknown class of exactly solvable time-dependent harmonic oscillators. The Caldirola-Kanai oscillator belongs to this class. For a general time-dependent harmonic oscillator, it is shown that choosing the dilatation parameter to satisfy the classical equation of motion, one obtains the solution of the Schrodinger equation. A simple generalization of this result leads to the reduction of the Schrodinger equation to a second-order ordinary differential equation whose special case is the auxiliary equation of the Lewis-Riesenfeld invariant theory. The time-evolution operator is expressed in terms of a positive red solution of this equation in a closed form, and the time-dependent position and momentum operators are calculated.PhysicsMathematical physicsJournal Article753247000145516