One-dimensional infinite square well potential

Qi Tang

First, this article explains the formula of one - dimensional infinitely deep square potential well's energy levels from stationary state schrodinger equation, and then deduces the same formula from one - dimensional half infinitely high square potential well' s energy levels diagram of graphic. solution, and proves that one - dimensional leveles are limit of one - dimensional half infinitely high square potential well' s energy levels. Finally it discusses the energy levels' number of one - dimensional half infinitely high square potential well and gives out the differentiateating formula about it.

Shi‐Hai Dong

H. Bartel Williams

Alberto G. Rojo, P. R. Berman

Abstract We address an interesting problem in elementary quantum mechanics, namely how can one obtain the momentum state eigenfunctions for the infinite square well potential as a direct solution of the time-independent Schrödinger equation in momentum space. The conventional method for obtaining the momentum state eigenfunctions for the infinite square well potential is to take the Fourier transform of the coordinate space eigenfunctions. Unfortunately, the Schrödinger equation in momentum space for the infinite well potential is not well-defined. As such we must use a potential whose Fourier transform is well-defined and then take a limit in which the potential approaches that of the infinite well potential. We present three approaches to the problem: one based on dimensional analysis, one in which the infinite well potential is viewed as the limit of a finite well whose depth approaches infinity, and one in which the infinite well potential is viewed as the limit of a power law potential in the limit that the power approaches infinity.

Xu Zhi-Jun, Shujuan Liu, Huang Lin +2 more

The evolution and collision of Bose-condensed gases in one-dimensional optical lattices are investigated in the presence of an infinitely deep square well created by two far-off resonant laser beams. The two far-off resonant laser beams are superimposed on the combined potential consisting of a magnetic trap and one-dimensional optical lattices. After the combined potential is switched off, the analytical result of the evolution of the density distribution of the Bose-condensed gas is given by using the propagator method. The collisions between the condensate and the infinitely deep square well are shown in the present work.

Pma Paul Mestrom