We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from the viewpoint of a Ermakov-type system. As an example, we consider a six-parameter family of the square integrable oscillator wave functions, which appears to be not obtainable by standard separation of variables. Finally, the invariance group of the generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schrödinger group of the free particle.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Mathematical Physics
- Condensed Matter Physics