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    • Determination of classical behaviour of the Earth for large quantum numbers using quantum guiding equation

      ALI SOLTANMANESH AFSHIN SHAFIEE

      Research Article Volume 93 Issue 4 October 2019 Article ID 0052

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      https://www.ias.ac.in/article/fulltext/pram/093/04/0052

    • Keywords

       

      Bohmian mechanics; quantum trajectories; correspondence principle

    • Abstract

       

      For quantum systems, we expect to see the classical behaviour at the limit of large quantum numbers. Hence, we apply Bohmian approach for describing the evolution of Earth around the Sun. We obtain possible trajectories of the Earth system with different initial conditions which converge to a certain stable orbit, known as the Kepler orbit, after a given time. The trajectories are resulted from the guiding equation $p = \nabla S$ in the Bohmian mechanics, which relates the momentum of the system to the phase part of the wave function. Except at some special situations, Bohmian trajectories are not Newtonian in character. We show that the classic behaviour of theEarth can be interpreted as the consequence of the guiding equation at the limit of large quantum numbers.

    • Author Affiliations

       

      ALI SOLTANMANESH1 2 AFSHIN SHAFIEE1 2

      1. Research Group on Foundations of Quantum Theory and Information, Department of Chemistry, Sharif University of Technology, P.O. Box 11365-9516, Tehran, Iran
      2. School of Physics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran

    • Dates

       
      Published
      1 October 2019
      Manuscript received
      29 August 2018
      Manuscript revised
      7 April 2019
      Accepted
      9 April 2019
      Early published
      Unedited version published online
      Final version published online
      12 July 2019

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