# 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: | 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?

## Experimental challenge: First detection of molecules

Go to the lab and follow the instructions. When you are done, return to this page and continue.

## Models

Test your knowledge!