A new approach to the symmetric rectangular quantum well: Analytic determination of well width from energy levels
C. Fouillant, Claude L. Alibert · American Journal of Physics · 1994
Many articles on the determination of the energy levels of a symmetric rectangular quantum well (SRQW) have been published in this Journal over the past 20 years. Standard textbooks of quantum mechanics as well as research papers offer graphical solutions. Exercises on quantum well (QW) remain rather difficult for students, because transcendental equations must be solved with boundaries at which the solution will be discontinuous. Numerical solutions generally determine the energy (En), assuming that the thickness is known, for each level number n. In this note, we show that the width L of an SRQW can be expressed directly as a function of the energy En for n=0,1,2,3,... .