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A proof for poisson bracket in non-commutative algebra of quantum mechanics

Khorasani, S ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. Publisher: EJTP Publisher , 2016
  3. Abstract:
  4. 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. © Electronic Journal of Theoretical Physics
  5. Keywords:
  6. Kramers-Kronig Identities ; Non-commutative algebra ; Poisson bracket ; Quantum mechanics
  7. Source: Electronic Journal of Theoretical Physics ; Volume 13, Issue 35 , 2016 , Pages 57-71 ; 17295254 (ISSN)
  8. URL: http://www.ejtp.com/articles/ejtpv13i35p57.pdf