# Waves? Particles? Quanta!!

Quantum objects display a behavior that is in conflict with our daily experience of macroscopic things. We distinguish three common models that are often invoked to describe certain aspects of reality.

## The particle model

Particles are often represented as balls to visualize small or even point-like objects with well-defined boundaries.

Their distinguishability is represented by different colors. Particles can be counted.

Classical particles can be localized. At any given moment they are at a given place which can be known in principle. They have a well-defined momentum, too. Within the model of Newtonian mechanics we can make precise predictions, where to find a particle in the future, if we are given exact initial conditions.

## Waves

Waves are spatially extended and periodic phenomena.

In the model of classical waves, their intensity can be continuously modified.

In practice even classical waves are composed of very many individual particles: water waves are result from the collective motion of very many molecules. Within one and the same wave different particles are at different locations and travelling with different momenta.

When two partial waves the superpose each other. The encounter of two wave crests leads to an even larger crest (constructive interference). When a crest overlaps with a trough the two waveforms may cancel each other (destructive interference).

## Quantum Physics

In quantum physics we can neither assign a precise position nor an exact direction to a particle.

However, the probability to find a quantum object at position $$x$$ with momentum $$p$$ can be predicted from the absolute square of the quantum mechanical wave function $$|\psi(x,p)|^2$$.

At any given time this probability can assume non-zero values at several even widely separated positions. In that case we say that the object is delocalized and we cannot assign a single well-defined position in space.

Interestingly, however, in any position measurement on that quantum object we find a single and whole object. Its properties, such as mass, energy, charge or polarizability are always united in this one object – not diluted or smeared over larger areas of space.

 Model: Quantum Particle Wave Detectors:

In free evolution quantum objects propagate according to Schrödinger’s wave equation. However, they interact with their environment as intact whole particles.

In our lab you can create a molecular beam and observe the molecules arriving on the detector, one by one. Which of the three models describes the observations best?