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    • A $\mathcal{PT}$ -symmetric simple harmonic oscillator

      ASTHA SINGH SUDHIR R JAIN

      Research Article Volume 92 Issue 4 April 2019 Article ID 0047

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/092/04/0047

    • Keywords

       

      $\mathcal{PT}$ symmetry; adiabatic invariance; oscillator

    • Abstract

       

      We consider a simple harmonic oscillator with non-Hermitian term and study it classically and quantummechanically. We conclude that this version of oscillator, which breaks parity and time reversal, displays all thefeatures possessed by the usual harmonic oscillator. In particular, we calculate its spectrum, adiabatic invarianceand Wigner functions, and show that there is a consistency between the classical and quantum descriptions.

    • Author Affiliations

       

      ASTHA SINGH1 SUDHIR R JAIN2 3 4

      1. Department of Physics, Institute of Science, Banaras Hindu University, Varanasi 221 005, India
      2. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400 085, India
      3. Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400 094, India
      4. UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Vidyanagari Campus, Mumbai 400 098, India

    • Dates

       
      Published
      1 April 2019
      Manuscript received
      18 March 2018
      Manuscript revised
      6 September 2018
      Accepted
      14 September 2018
      Early published
      Unedited version published online
      Final version published online
      15 February 2019

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