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

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    • 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



      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

  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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