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The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics. (English) Zbl 1357.81080
Summary: The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems.

MSC:
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81-03 History of quantum theory
01A60 History of mathematics in the 20th century
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