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Journal of Statistical Physics

Expectation Values of Observables in Time-Dependent Quantum Mechanics

Jean-Marie Barbaroux, Alain Joye

Published Mar 1, 1998• 14 citations
Publisher
DOI
10.1023/a:1023279311564

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Quantum mechanics is challenging even for advanced undergraduate and graduate students.In the Schrödinger representation, the wave function evolves in time according to the time dependent Schrödinger equation.The time dependence of the wave function gives rise to time dependence of the expectation value of observables.We have been exploring the difficulties that advanced undergraduate and graduate students have with time dependence of expectation values in quantum mechanics.We have developed and administered conceptual free response and multiplechoice questions to students to investigate these difficulties.We also interviewed 23 students individually using a thinkaloud protocol to obtain a better understanding of the rationale behind students' written responses.We find that many students struggle with time dependence of expectation values of observables.We discuss some findings.
Quantum information-theoretic approach had been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However, there hasn’t been enough advancement or rigorous development of the subject. In the following paper we try to find the relationship between a general quantum mechanical observable and von Neumann entropy. We find that the expectation values and the uncertainties of the observables have bounds which depend on the entropy. The results also show that von Neumann entropy is not just the uncertainty of the state but also encompasses the information about expectation values and uncertainties of any observable which depend on the observers choice for a particular measurement. Also a reverse uncertainty relation is derived for [Formula: see text] quantum mechanical observables.