A wave function is a mathematical description that captures all the possible states a quantum system could be found in, along with the probability of each. It is usually written as the Greek letter psi, and it does not describe where a particle is, it describes the odds of finding it in any given place if you look.
Squaring the wave function gives you a probability distribution. Before a measurement, a particle described by a wave function is not secretly in one location waiting to be discovered, it is genuinely spread across every possibility the function allows.
The moment a measurement happens, the wave function appears to collapse to a single outcome. What actually causes that collapse, and whether it is a real physical process or just an update to our knowledge, is one of the oldest open questions in physics, central to debates about what quantum mechanics really means.
The wave function’s behavior over time is governed by the Schrodinger equation, formulated by Erwin Schrodinger in 1926, which plays a role in quantum mechanics comparable to Newton’s laws in classical physics, predicting exactly how the wave function evolves moment to moment as long as no measurement interrupts it. Turning that wave function into an actual probability requires one more step, called the Born rule, proposed by physicist Max Born, which says the probability of finding a particle in a particular location equals the square of the wave function’s value there. Together, these two pieces let physicists calculate, with extraordinary precision, the odds of any measurable outcome in a quantum system, even though the wave function itself describes something that can never be observed directly, only inferred from the statistics of many repeated measurements.
Physicists remain divided over how to interpret what the wave function’s collapse actually represents. The Copenhagen interpretation, the oldest and historically most taught view, treats collapse as a genuine physical event triggered by measurement, while the many-worlds interpretation instead argues the wave function never collapses at all, and every possible outcome simply plays out in a separate, branching version of reality that we never perceive the others of.