Entangled with Quantum Mechanics

1
Entangled with Quantum Mechanics

• Understanding student difficulties in first year
  quantum mechanics courses

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 Heisenbergs 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_at_science.uva.nl