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A Quantum Mechanical Game of Craps: Teaching the Superposition Principle Using a Familiar Classical Analog to a Quantum Mechanical System

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Patrick E. Fleming

Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287

J. Chem. Educ., 2001, 78 (1), p 57

DOI: 10.1021/ed078p57

Publication Date (Web): January 1, 2001

Section:

History, Education, and Documentation

Abstract

A standard die makes an ideal classical analog to a quantum mechanical system. In this paper, the relationships between an operator, wave functions that are eigenfunctions of the operator, and the corresponding eigenvalues are discussed. While the form of neither the operator nor the total wave function is known, the properties and expectation values for measurements on the system can be predicted. The connection between quantum mechanics and probability is explored using both "normal" and "loaded" dice. Using the orthonormality of the wave functions, the familiar result for the probability of rolling a single value and the expected average value for a large number of rolls are derived. The collapse of the wave function upon measurement of the system, which is analogous to the collapse of the probability distribution upon the die coming to rest, is also discussed.