Author(s)

Akihiro Ogura

Laboratory of Physics, Nihon University, Matsudo, Japan.

The quantum mechanical relationships between time-dependent oscillators, Hamilton-Jacobi theory and an invariant operator are clarified by making reference to a system with a generalized oscillator. We introduce a linear transformation in position and momentum, and show that the correspondence between classical and quantum transformations is exactly one-to-one. We found that classical canonical transformations are constructed from quantum unitary transformations as long as we are concerned with linear transformations. We also show the relationship between the invariant operator and a linear transformation.

Quantum Canonical Transformation, Linear Transformation, Generalized Oscillators, Invariant Operator

Ogura, A. (2016) Classical and Quantum Behavior of Generalized Oscillators in Terms of Linear Canonical Transformations. Journal of Modern Physics, 7, 2205-2218. doi: 10.4236/jmp.2016.715191.