TITLE:
Classical and Quantum Behavior of Generalized Oscillators in Terms of Linear Canonical Transformations
AUTHORS:
Akihiro Ogura
KEYWORDS:
Quantum Canonical Transformation, Linear Transformation, Generalized Oscillators, Invariant Operator
JOURNAL NAME:
Journal of Modern Physics,
Vol.7 No.15,
November
29,
2016
ABSTRACT: 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.