Abstract
Abstract The quantum problem of stationary states of a particle in a box is revisited by means of the unilateral Fourier transform. Homogeneous Dirichlet boundary conditions demand a finite Fourier sine transform which is actually the Fourier sine series.
Highlights
In quantum theory, a particle confined by impenetrable walls is usually called a particle in box
The choice of sine or cosine transform is decided by the homogeneous boundary conditions at the origin: Dirichlet condition ( f (x)|x=0 = 0) or Neumann condition ( df (x) /dx|x=0 = 0)
We have shown that the stationary states of the particle in a box via unilateral Fourier transform can be found with simplicity because it is a tool that favors compliance with boundary conditions from the start
Summary
A particle confined by impenetrable walls is usually called a particle in box. For onedimensional cases that kind of system is modeled by an infinite square-well potential. This is one of the easiest problems in quantum mechanics exhibiting many characteristics of the quantum physics and for this reason it appears in a plethora of introductory textbooks on quantum mechanics In a recent paper diffused in the literature, the quantum problem of a particle in an infinite square-well potential was claimed to be solved via Laplace transform [13]. [13] awakens interest in applying over a finite interval other kinds of integral transforms usually defined over an infinite or a semi-infinite range of integration. In this work we approach the quantum problem of a particle in an infinite square-well potential with the unilateral Fourier transform. That kind of finite unilateral Fourier transform, and its close connection with Fourier series, can be of interest of teachers and stu-
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