On the Harmonic Oscillator Group
Abstract: We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a viewpoint of the Ermakov-type system. A six parameter family of the square integrable oscillator wave functions, which seems cannot be obtained by the standard separation of variables, is presented as an example. The invariance group of the generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schrodinger group of the free particle.
Exact Wave functions for Harmonic Oscillators
The recent publication of the article "Exact Wave functions for Harmonic Oscillators" which was a post-result of presenting work in Brazil this past May and finding collaborations there.
Also, the following comes from the editors from the Journal of Russian Laser Research: "Another 'immortal' area, where nonetheless new results can still be discovered, is related to the dynamics of quantum oscillators or more general quantum systems with quadratic Hamiltonians. It is represented by the papers of Sergei Suslov with their coauthors."