Quantum mechanical observables under a symplectic transformation of coordinates

We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $\mathbb{R}^q$. Using the formalism of rigged Hilbert spaces, we define eigenstates for all the observables. Then we work out the explicit form of the corresponding transformation of these eigenstates. A few examples are included at the end of the paper.

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This work was supported by Charles University Grant Agency [Project No. 906419].

Published 30 October 2023