wavefunction

If a particle does not have a definite position, how do we describe where it is? The answer quantum physics gives is a kind of smeared-out cloud of possibility, thicker where the particle is more likely to be found and thinner where it is less likely. This cloud is captured by a mathematical object called the wavefunction, usually written with the Greek letter psi. It is the most complete description quantum theory gives of a single particle or system.

The wavefunction is not directly the probability; it is one step removed. Its squared size at each point gives the probability of finding the particle there if you look. Where the wavefunction is large, you are likely to find the particle; where it passes through zero, you will never find it. Crucially, the wavefunction can ripple, spread, overlap with itself, and even cancel itself out where two parts meet out of step — and that self-cancellation is exactly what produces interference patterns. The wavefunction evolves smoothly and predictably over time according to the Schrodinger equation, right up until you make a measurement, at which point the cloud appears to collapse to wherever the particle is actually found.

In particle physics the wavefunction (and its relativistic, field-theoretic descendants) is the bookkeeping device for everything you can predict. It encodes a particle's possible positions, momenta, spins, and the chances of one particle turning into others in a collision. Be careful with the picture, though: the wavefunction is not a physical fog you could scoop up, and squaring it gives probabilities, not the particle itself. Exactly what the wavefunction is — a real thing, or only our information about a system — remains one of the genuinely open questions in the interpretation of quantum mechanics.