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

Resonance

article

V Balakrishnan¹ 

[1] Department of Physics, Indian Institute of Technology

关键词: Quantum mechanics;    continuous symmetry;    curved surfaces;    in­verse problem;    spectrum;    do­main;    isometry;    isospectral domains;    eigenvalues.;   

DOI  :  10.1007/s12045-022-1429-8

学科分类：社会科学、人文和艺术（综合）

来源: Springer

【 摘 要 】

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.

【 授权许可】

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