Related papers: Quantum Mechanical Observables under a Symplectic Transformation of Coordinates

Quantum Mechanical Observables under a Symplectic Transformation of Coordinates

URL: http://arxiv.org/abs/2007.10858v2
Date: Tue, 16 Mar 2021 15:56:46 GMT
Title: Quantum Mechanical Observables under a Symplectic Transformation of Coordinates
Authors: Jakub K\'aninsk\'y
Abstract summary: We consider a general symplectic transformation of quantum-mechanical observables in a quantized version of a finite-dimensional system. Using the formalism of rigged Hilbert spaces, we define eigenstates for all the observables.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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