Quantum Mechanical Observables under a Symplectic Transformation of Coordinates

Jakub Káninský

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arXiv · 2007.10858

Quantum Mechanical Observables under a Symplectic Transformation of Coordinates

Jakub Káninský

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Abstract

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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Jakub Káninský. 2020-07-21. Quantum Mechanical Observables under a Symplectic Transformation of Coordinates. https://arxiv.org/abs/2007.10858

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