Preprint Article Version 1 This version is not peer-reviewed

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.

Journal reference: Entropy 2018, 20, 869
DOI: 10.3390/e20110869

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.

Subject Areas

Born-Jordan, quantization, short time propagator

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