High School Teachers at CERN
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Teaching Modern Physics in Dutch High Schools

Three levels of conceptual difficulty:
1. Wave / particle duality with ensuing difficulties with respect to imagining what physical reality is like
2. The logical structure of QM assigning amplitudes to logical possibilities general superposition principle complementarity (Bohr) quantum logic(s) (Reichenbach, Von Neumann, and many others).
3. Entangled States. Schrödinger's cat, Wigner's friend. Einstein-Podolsky-Rosen, Bell inequalities
 
Problem:
At a high school level, students should stay clear of level 2 and 3, but the wave / particle duality cannot be avoided, and already provides major difficulties.

Suggestion:
Turn it into a major issue that receives proper time and attention

Starting points:
  * Take wave / particle duality as a central theme.
* Minimize the level of mathematical difficulty.
* Produce a core program, with possible add-ons.

Problem:
Any approach taking the wave / particle duality as a serious theme can count on a great deal of initial skepticism and disbelief. In order to counteract disbelief and other forms of frustration:
* Show concrete and convincing applications
* Pay attention to the relations between microscopic and macroscopic phenomena, and between the description of matter at different scales (molecules, atoms, nuclei, particles, ...)
* Stress the importance for other fields, such as chemistry, electronics, material science, etc.
 
Problem:
* How can one reduce the level of mathematical difficulty?
* What kind of things should be contained in the core, what things should be optional?

Some examples:
* In order to minimize mathematical difficulties, the Schrödinger equation is not included in the core. After all, introducing a 'quantum picture' of matter is not the same as an introduction to quantum mechanics. However, for interested students there is an optional add-on, for which separate credits can be given.
* Only a small module about subatomic particles is included in the core with only one generation of quarks and leptons, and with limited attention for interaction particles. Emphasis on the use of conservation laws.

Again, some more can be added as optional:
* The "particle in a box" model is included because it can be introduced on basis of what students know about standing waves, without having to introduce a wave equation.
* The core also includes some simple applications of the "particle in a box" model providing links to various macroscopically observable phenomena and to chemistry.

Program Outline.

1. Structure of matter
 
* Introduction to wave / particle duality PE-effect, De Broglie waves, electron diffraction, probability and amplitude
* Particle in box - model photon between two mirrors, electron in copper wire, (preliminary) atomic model p = h / ? = nh / 2L E = p2 / 2m = n2 h2 / 8mL2
* Refinement: potential wells, H-atom (qualitatively), tunneling
* Application to real life phenomena: hardness of metals (electron pressure, Pauli principle), electron shells and atomic bonding, the spectrum of organic dyes
 
2. Reaction Processes
 
* Change
* reaction equations
* macroscopic
* chemical
* physical)
* conservation principles
* varying from rules like the 'conservation of car keys' to laws like conservation of momentum
* Various kinds of reactions
* colliding cars, ...
* atoms and molecules
* Use of E = mc2,
* nuclear reactions
* subatomic particles
* no details about interactions
* only one generation of leptons
 
3. Interpretation
 
* Indeterminacy
* Wave packets
* Heisenberg qualitatively
* Reduction of the wave packet
* measurement disturbance
* delayed choice experiment
* Similarity / difference between radiation and matter
* wave and particle models
* application to matter and radiation
 
 
further information:  www.phys.uu.nl/~wwwpmn
e-mail:   d.j.hoekzema@phys.uu.nl

© CERN and High School Teachers Programme at CERN	Last modified: 28 June 2002