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Entangled with Quantum Mechanics

Understanding student difficulties in first year quantum mechanics courses. Entangled with Quantum Mechanics. Lodewijk Koopman, Wolter Kaper, Ton Ellermeijer AMSTEL Institute, Faculty of Science. Introduction. “I think I can safely say that nobody understands Quantum Mechanics”

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Entangled with Quantum Mechanics

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  1. Understanding student difficulties in first year quantum mechanics courses Entangled with Quantum Mechanics Lodewijk Koopman, Wolter Kaper, Ton Ellermeijer AMSTEL Institute, Faculty of Science

  2. Introduction “I think I can safely say that nobody understands Quantum Mechanics” Richard Feynman Should we expect students to understand it?

  3. Overview research • Four year PhD project • Improve teaching in quantum mechanics (locally) • Contribute to research on physics education • First year: • Find out what students find difficult • Understand why they find this difficult • Literature search • Observation of two courses • Questionnaire • Create hypotheses

  4. The courses First year, 2nd semester, 14 weeks • Quantum Physics • Lectures: 45 students • Tutorial sessions: three groups of 15 students • Textbook: D.J. Griffiths, Introduction to quantum mechanics, 2005 • Topics: principles, Schrödinger equation, uncertainty relation, stationary states, several potentials • Quantum Chemistry • Lectures: 15 students • Tutorial sessions and Spartan project: one group • Textbook: Atkins and de Paula, Atkins’ Physical Chemistry, 2002 • Topics: + time-independent Schrödinger equation, atomic and molecular structure

  5. Quantum vs. classical mechanics • Understanding of certain classical concepts Energy and potential energy “Yeah well, the particle does not really have negative energy. That is a somewhat vague notion.” • Know what is classically expected Relate tunneling to classical result • Obstructive conceptions Determinism: “But why can't we just determine where this particle is? Doesn't it follow a certain trajectory?”

  6. Difficulties with Heisenberg’s uncertainty relation Two definitions used By teachers: simultaneous measurement of position and momentum In textbooks: spread in position and momentum Students: Interpret this as uncertainty because of measurement error Show a hybrid view on the meaning of the relation

  7. Interpretation of quantum mechanics Born's statistical interpretation of the wave function Copenhagen interpretation wave function has different meaning in interpretation and when doing measurements “But when you have one particle, it then is possible to have an interference pattern, only you cannot measure it?” projection postulate “But you will always find a peak when you measure? Because if you measure a particle, then its wave function is always …”

  8. Conclusion Students: do not master necessary classical concepts hold onto a deterministic world view have a contradictory view of quantum mechanics have difficulties with the Copenhagen interpretation do not have a mental picture of what is taught

  9. Future research Possible topic role of interpretation of quantum mechanics: “What impact does the use of the Statistical Interpretation of quantum mechanics have on the understanding of quantum mechanics?” Next steps Team up with teachers: what do we change? Design and observe education Conditions cooperation with teachers motivate students to study basic mathematical skills

  10. “If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet.” Niels Bohr Suggestions and questions are most welcome! For more information, please see paper Contact: lkoopman@science.uva.nl

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