• Wave packet construction in three-dimensional quantum billiards: Visualizing the closed orbit, collapse and revival of wave packets in the cubical billiard

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    • Keywords

       

      Three-dimensional bound systems; revivals and collapses; quantum mechanics.

    • Abstract

       

      We examine the dynamical evolution of wave packets in a cubical billiard where three quantum numbers (𝑛𝑥, 𝑛𝑦, 𝑛𝑧) determine its energy spectrum and consequently its dynamical behaviour. We have constructed the wave packet in the cubical billiard and have observed its time evolution for various closed orbits. The closed orbits are possible for certain specific values of quantum numbers (𝑛𝑥, 𝑛𝑦, 𝑛𝑧) and initial momenta (𝑘𝑥, 𝑘𝑦, 𝑘𝑧). We observe that a cubical billiard exhibits degenerate energy levels and the path lengths of the closed orbits for these degenerate energy levels are identical. In spite of the identical path lengths, the shapes of the closed orbits for degenerate levels are different and depend upon angles 𝜃 and 𝜙 which we term as the sweep and the elevation angles, respectively. These degenerate levels owe their origin to the symmetries prevailing in the cubical billiard and these levels disappear completely or partially for a parallelepiped billiard as the symmetry breaks due to commensurate or incommensurate ratio of sides.

    • Author Affiliations

       

      Maninder Kaur1 2 Bindiya Arora1 Mahmood Mian1

      1. Department of Physics, Guru Nanak Dev University, Amritsar 143 005, India
      2. Department of Physics, D.A.V. College, Amritsar 143 005, India
    • Dates

       
  • Pramana – Journal of Physics | News

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