Particle in an infinite smooth well

Authors

  • Andrei Smirnov Universidade Federal de Sergipe
  • Antonio Jorge Dantas Faria Junior Universidade Federal de Sergipe

Keywords:

Schrödinger equation, infinite smooth well, Darboux transforms

Abstract

In this paper it is considered a particle in an infinite potential well of special smooth form. To obtain eigenfunctions and eigenvalues of the problem, a method of Darboux transformations is applied. An orthonormal set of the eigenfunctions is presented. Some important properties of the eigenfunctions are shown. Principal characteristics of the particle in the well are discussed. A function of distribution of the probability density is analyzed. Conditions for determination of points of extrema of the probability density are formulated and corresponding transcendental equations are presented. An approximated method for determination of points of extrema is also proposed. Expected values of position and momentum of the particle are calculated explicitly. For some lower energy states, distributions of probability density are shown graphically in comparison with distributions for the infinite square well. As an additional useful result, some integrals of special combinations of trigonometric functions are presented.

Author Biographies

Andrei Smirnov, Universidade Federal de Sergipe

Departamento de Fisica, UFS

Antonio Jorge Dantas Faria Junior, Universidade Federal de Sergipe

Departamento de Fisica, UFS

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Published

2015-03-06

How to Cite

Smirnov, A., & Faria Junior, A. J. D. (2015). Particle in an infinite smooth well. Scientia Plena, 11(3). Retrieved from https://www.scientiaplena.org.br/sp/article/view/1680

Issue

Vol. 11 No. 3 (2015): March/Março 2015

Section

Articles

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