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arXiv · 1411.1338

A Proof for Poisson Bracket in Non-commutative Algebra of Quantum Mechanics

Sina Khorasani
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Abstract

The widely accepted approach to the foundation of quantum mechanics is that the Poisson bracket, governing the non-commutative algebra of operators, is taken as a postulate with no underlying physics. In this manuscript, it is shown that this postulation is in fact unnecessary and may be replaced by a few deeper concepts, which ultimately lead to the derivation of Poisson bracket. One would only need to use Fourier transform pairs and Kramers-Kronig identities in the complex domain. We present a definition of Hermitian time-operator and discuss some of its basic properties.

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Sina Khorasani. 2014-11-05. A Proof for Poisson Bracket in Non-commutative Algebra of Quantum Mechanics. https://arxiv.org/abs/1411.1338

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