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

被引:0
作者
V. Balakrishnan
机构
[1] Indian Institute of Technology,Department of Physics
来源
Resonance | 2022年 / 27卷
关键词
Quantum mechanics; continuous symmetry; curved surfaces; inverse problem; spectrum; domain; isometry; isospectral domains; eigenvalues;
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学科分类号
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.
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页码:1327 / 1340
页数:13
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