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      https://www.ias.ac.in/article/fulltext/pram/073/06/0969-0988

    • Keywords

       

      Twin symmetric barrier; quasi-bound states; resonant tunnelling.

    • Abstract

       

      In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in one-dimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit–Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit–Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.

    • Author Affiliations

       

      A Uma Maheswari1 P Prema1 S Mahadevan1 C S Shastry1

      1. Department of Sciences, Amrita Vishwa Vidyapeetham, Ettimadai, Coimbatore 641 105, India
    • Dates

       
  • Pramana – Journal of Physics | News

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