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Deriving relativistic Bohmian quantum potential using variational method and conformal transformations

Rahmani, F ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1007/s12043-015-1076-7
  3. Abstract:
  4. In this paper we shall argue that conformal transformations give some new aspects to a metric and changes the physics that arises from the classical metric. It is equivalent to adding a new potential to relativistic Hamilton-Jacobi equation. We start by using conformal transformations on a metric and obtain modified geodesics. Then, we try to show that extra terms in the modified geodesics are indications of a background force. We obtain this potential by using variational method. Then, we see that this background potential is the same as the Bohmian non-local quantum potential. This approach gives a method stronger than Bohm's original method in deriving Bohmian quantum potential. We do not use any quantum mechanical postulates in this approach
  5. Keywords:
  6. Bohmian quantum mechanics ; Non-locality ; Quantum potential ; Ordinary differential equations ; Quantum theory ; Conformal transformation ; Hamilton - Jacobi equations ; Nonlocal ; Nonlocalities ; Quantum mechanical ; Quantum potentials ; Variational methods ; Conformal mapping
  7. Source: Pramana - Journal of Physics ; Volume 86, Issue 4 , 2016 , Pages 747-761 ; 03044289 (ISSN)
  8. URL: https://link.springer.com/article/10.1007/s12043-015-1076-7