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

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 func...

Full description

Saved in:
Bibliographic Details
Published in:Journal of chemical education 2001-01, Vol.78 (1), p.57
Main Author: Fleming, Patrick E
Format: Article
Language:English
Subjects:
Born, Max (1882-1970)
Chemistry
Einstein, Albert (1879-1955)
Game theory
Mechanical systems
Organic chemistry
Quantum chemistry
Quantum mechanics
Quantum theory
Science education
Superposition (mathematics)
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0021-9584
1938-1328
DOI:10.1021/ed078p57