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The Chemical Educator

ISSN: 1430-4171 (electronic version)

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Abstract Volume 16 (2011) pp 168-174

Particle a in One-Dimensional Finite and Semi-Infinite Well Revisited

Enrique Peacock-López

Department of Chemistry, University of Cape Town, Rondebosch, 7701 South Africa,
Received May 25, 2010. Accepted February 27, 2011.

Published: 15 July 2011

Abstract. For the quantum particle in a finite and semi-infinite 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

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