A Proof for Poisson Bracket in Non-commutative Algebra of Quantum Mechanics
Quantum Physics
2016-04-12 v5
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.
Keywords
Cite
@article{arxiv.1411.1338,
title = {A Proof for Poisson Bracket in Non-commutative Algebra of Quantum Mechanics},
author = {Sina Khorasani},
journal= {arXiv preprint arXiv:1411.1338},
year = {2016}
}