The Chemical EducatorISSN: 14304171 (electronic version) Abstract Volume 16
(2011) pp 168174 Particle a in OneDimensional Finite and SemiInfinite Well RevisitedEnrique PeacockLópez Department of Chemistry, University of Cape Town,
Rondebosch, 7701 South Africa, epeacock@williams.edu Published: 15 July 2011 Abstract. For the quantum particle in a finite and semiinfinite well, we scale space and energy to consider a dimensionless Schrödinger equation that can be solved for the allowed energy levels. In contrast to traditional approaches that determine the energies from dimensional transcendental equations associated with the boundary conditions, we solve for the square root of the dimensionless energies, which are also solutions of dimensionless transcendental equations. Our ability to define classes of wells depends on the value of the square root of the dimensionless well depth. We are also able to determine the maximum number of energy levels quite easily, and, besides deriving the relevant transcendental equations, we obtain asimple expression for the corresponding wave functions, which can be plotted using the numerical values of the allowed energies.
Key Words: In the Classroom; physical chemistry; quantum mechanics (*) Corresponding author. (Email: epeacock@williams.edu) Article in PDF format (157 KB) HTML format
