Localization and Spread of the Particle in a Box

TCE

The Chemical Educator

ISSN: 1430-4171 (electronic version)

Table of Contents

Abstract Volume 7 Issue 2 (2002) pp 71-73

Localization and Spread of the Particle in a Box

Jan J. C. Mulder

Gorlaeus Laboratories, Leiden University, 2300 RA Leiden, The Netherlands
Received November 3, 2001. Accepted February 27, 2002

Published online: 22 March 2002

Abstract. The most basic example of a quantum mechanical problem, the one-dimensional particle in a box, is revisited. Three aspects are treated. 1.It is shown that a number of textbooks give an incorrect result for the expectation value of x², and, therefore, do not obtain the correct spread Dx. Consequently, the verification of the Heisenberg relation is also in error. 2. It is found that textbooks do not mention the origin dependence of expectation values, which is a nuisance, as the problem is evidently treated in the literature with two choices of origin. 3. Superposition of an infinite number of even (cosine) solutions of the one-dimensional particle in the box allows for an analytical demonstration of complete localization of the particle (Dx = 0).

Key Words: In the Classroom; physical chemistry; quantum mechanics; particle in a box

(*) Corresponding author. (E-mail: j.mulder@chem.leidenuniv.nl)

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