Continuous limit of the square well problem in quantum mechanics
arXiv:2607.13872
summary
The paper demonstrates how the solutions of the quantum square‑well potential converge to free‑particle solutions as the well width becomes infinite, using a Fourier‑transform based analysis of the wave equation.
Abstract
The free-particle and square-well potentials are two of the most emblematic problems in quantum mechanics, illustrating essential concepts such as matter waves, energy quantization, and bound states. It is therefore natural to consider how the free-particle solutions emerge from the square well as the width approaches infinity. In this work, we present a systematic procedure to demonstrate this transition by applying a Fourier transform to the wave equation.
7 pages, 2 figures
Topics & keywords
#square well potential#free particle#quantum mechanics#fourier transform#bound states#energy quantizationsquare wellfree particleFourier transformcontinuous limitwave equationbound states