Probability Distribution of Momenta in an Infinite Square-Well Potential

Andrée Johannin-Gilles, René Abjean, Yves Guern +1 more

S. A. Fulling

David Thompson

Shi‐Hai Dong, Guo-Hua Sun, Yu Jiang

The Wigner distribution function for a quantum system with an infinitely deep square-well potential is obtained analytically and presented by plotting the Wigner distribution functions on the quantum phase space. The cross-matrix elements of the expectation values of some classical quantities are also obtained. The case of the symmetrical square-well potential is studied briefly.

Andrei Smirnov, Antonio Jorge Dantas Faria

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.

Jan Naudts