• Classical limit of relativistic quantal system with attractive Coulomb interaction

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/036/03/0271-0288

    • Keywords

       

      Klein-Gordon equation for relativistic Coulomb problem; coherent state for harmonic oscillator; perhelion precession; dispersion with time

    • Abstract

       

      Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r2〉 − 〈r2]1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.

    • Author Affiliations

       

      Swagata Nandi1 C S Shastry1

      1. Department of Physics, North-Eastern Hill University, Shillong - 793 003, India
    • Dates

       
  • Pramana – Journal of Physics | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2017-2019 Indian Academy of Sciences, Bengaluru.