Particle in a one-dimensional box

ANJALI JANGID, Pooja Devi, Aniruddha Chakraborty

James M. Feagin

Caio Lima Firme

This chapter discusses the problem of one particle in a one-dimensional box free of the potential energy inside the box, that is, no external force is exerted on the particle inside the box. The corresponding Schrödinger equation is given along with the boundary conditions which yields an elliptic second-order differential equation and the solutions are given next: the wave function, quantum numbers and corresponding energy. The normalized wave function is also given which is similar to that of the one-particle harmonic oscillator. Afterwards, the Hamiltonian function of the particle in a bidimensional box is given along with its wave function that is the product of two wave function of the particle in a one-dimensional box and the energy is the sum of two energy components, x and y, of the particle in a one-dimensional box. Finally, there is a couple of exercises to plot the wave functions of a rectangular box to find the probability density of the wave function for a symmetrical box. (164 words).

Boutheina Boutabia-Chéraitia, Abdenacer Makhlouf

Abstract In this article, we study a relativistic DKP particle in a one-dimensional box. We prove that it is impossible that the wavefunction vanishes completely at the box walls and provides various boundary conditions for this problem.

Sungwoon Kim

An elementary method for the calculation of the momentum autocorrelation function of a particle in a one-dimensional box is presented.