Electrons behaving as waves

Students will know that electrons carry energy and momentum when they are moving. Yet these moving electrons seem to be guided to an interference pattern just like waves of light; or just like photons of light in the micro-physical world.

In the macro-physical world, large particles such as tennis balls and people do not display wave behaviour; wavelengths associated with such particles, at usual speeds, are so extremely minute that it won’t be possible to observe the diffraction or interference pattern associated with them. Nevertheless the behaviours of waves and particles in the micro-physical world are not entirely separate. Moving particles do follow wave directions, and it is the wave which predicts a probability of where to find the particle. The particles are guided by ‘matter waves’. Wave-particle duality was first suggested by Louis de Broglie about a century ago.

This raises the question of whether electrons (and other tiny particles) are particles or waves. Many observations in atomic physics can be treated using the particle model on its own. Others require the wave model. Both models prove to be useful and, despite their contradictory nature, must both be used for a full description. The two aspects of the electron both contradict and complement one another: both aspects are needed for a complete description. Niel’s Bohr’s solution was the principle of complementarity

The Complementarity Principle says that sometimes electrons have the properties of particles and sometimes the properties of waves, but never both together. Their two types of behaviour complement each other but never coexist. The type of behaviour that is shown usually depends on the measurement technique being used. To put it another way, ask a wave-type question and you will get a wave’s answer. Ask a particle-type question and you will get a particle’s reply.

Bohr’s interpretation was that the two irreconcilable descriptions should be applied in turn but cannot be applied simultaneously. They are never in direct conflict, because it is impossible to determine at the same time all the information required to make the two images precise.

This relates to Heisenberg’s Uncertainty Principle. The more precise the observations of one picture, the less precise the other becomes. Define the wavelength of an electron sharply enough and the attempt to apply the particle model will surely fail. Localize the electron definitely enough and the wave model fails.