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Journal of Chemical Education

On introducing the uncertainty principle

G. M. Muha, D. W. Muha

Published Jun 1, 1986• 1 citation
Publisher

Abstract

Because if the strong mathematical flavor of the Heissenberg's Uncertainty Principle, the essence and significance of this argument is often lost on beginning students. These authors present an alternative introduction to the topic that allows students to gain a more intuitive understanding.
DOI
10.1021/ed063p525

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Most engineers need a basic understanding of quantum mechanics, and for this the typical college introduction is enough. Such an introduction tends to be axiomatic but physically unenlightening. The rules of quantum mechanics (QM) are a fait accompli; justified because they work. This is a good beginning, but those needing to learn more face a special quantum barrier: more advanced texts often continue in the axiomatic tradition. Infinite-dimensional spaces, amplitude vectors, matrices, and operators in lieu of momentum and energy-these and other concepts may be introduced with little rationalization or intuition. To an inquiring student, QM can quickly become bizarre; something to be manipulated but not understood. This need not be so. Here the authors present one teaching solution. They show that many of QM's key ideas can be reasoned out from just a few physical assumptions with mathematics that is low in dimension, linear and accessible to many. Some results include a simple reason for believing probability amplitudes are more natural to use than probabilities, the duality of functions as vectors and vice versa, an example of how a matrix, an operator and a physical value might be related, the Heisenberg uncertainty principle and Schrodinger's equation.
Internalization of the Heisenberg uncertainty principle is a key first step in learning and understanding the wave-particle duality of matter, which is at the core of quantum mechanics, but can be difficult to comprehend due to the examples traditionally employed. A new model for introducing the Heisenberg uncertainty principle to upper-level undergraduates is presented. The fundamental physics underlying the uncertainty between momentum and position (or frequency and time) is demonstrated via analogy to familiar acoustical examples, allowing students to hear the effects of the uncertainty principle. Thunder serves as a particularly intuitive example, illustrating both the lower bound of certainty and situations in which the actual uncertainty is greater than the limit dictated by Heisenberg. Additionally, a simple mathematical model is presented to illustrate the trade off between uncertainty in frequency and in time.
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