• Particle in a Box: A Basic Paradigm in Quantum Mechanics - Part 2

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    • Keywords


      Quantum mechanics, continuous symmetry, curved surfaces, in­verse problem, spectrum, do­main, isometry, isospectral domains, eigenvalues.

    • Abstract


      The problem of a particle moving freely inside a region with rigid, perfectly reflecting walls serves as a paradigm to illus­trate numerous aspects of quantum mechanics (QM). In Part 11 of this two-part article, we discussed several of these as­pects using, respectively, a line segment, a ring, and a square as the region concerned. In the present part, we shall consider the cases of a circular region and a surface of constant posi­tive curvature (a sphere). We shall then comment on the gen­eral case of a dynamical billiard. Finally, we turn to the in­verse problem: given the energy spectrum of a particle mov­ing freely inside a region, what can be deduced about the geo­metrical properties of the region? Some important results in this regard will be described in brief.

    • Author Affiliations


      V Balakrishnan1

      1. Department of Physics, Indian Institute of Technology, Madras, Chennai 600036, India.
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