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Short-Time Propagators and the Born--Jordan Quantization Rule
Version 1
: Received: 14 October 2018 / Approved: 16 October 2018 / Online: 16 October 2018 (08:59:09 CEST)
A peer-reviewed article of this Preprint also exists.
de Gosson, M.A. Short-Time Propagators and the Born–Jordan Quantization Rule. Entropy 2018, 20, 869. de Gosson, M.A. Short-Time Propagators and the Born–Jordan Quantization Rule. Entropy 2018, 20, 869.
Abstract
We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born--Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.
Keywords
Born-Jordan, quantization, short time propagator
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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