Quantum Wavefunction

Picture of a wall in front of a building with modern architecture. The wall of polished marble is inscribed with mathematical equations.
Schrödinger equation as part of a monument in front of Warsaw University's Centre of New Technologies. Halibutt / Wikimedia Commons / CC-BY-SA 3.0

Definition:

The quantum wavefunction is a way of representing the physical possibilities within quantum physics. The wavefunction is something called a "state vector" and it represents the physical parameters of a particle (or a set of particles) as a set of numbers. In a real sense, the particles themselves are the set of numbers described by the quantum wavefunction.

The wavefunction equation was developed by Erwin Schrodinger, and so it is called the Schrodinger equation.

The Schrodinger equation represents how the quantum wavefunction changes over time. In this formalism, the quantum wavefunction is typically represented by lower-case and uppercase Greek letters psi: ψ and Ψ.

The quantum wavefunction is not strictly speaking a result of quantum physics, but rather one of the fundamental concepts upon which the mathematical formalism of quantum physics is built. The existence of the quantum wavefunction is assumed and then its reality is demonstrated by the fact that making this assumption leads to predictions which conform well with physical reality through the results of quantum experiments and measurements of quantum phenomena.

Quantum physics works by representing all possible outcomes as a superposition of quantum states. The wavefunction is a complex function (a function containing quantities that are complex numbers) and is constructed in such a way that performing an operation to take the modulus of the complex function for a given state results in a real value that represents the probability density of a result that corresponds to that state.

This is how the quantum wavefunction is transformed into a meaningful physical prediction. The process of transitioning from a general quantum wavefunction into a definite value for a specific state is typically called the "collapse of the wavefunction."

What Does the Quantum Wavefunction Mean?

The physical meaning of the quantum wavefunction and the proper fundamental understanding of it is one of the major controversies within theoretical quantum physics.

Though it is bizarre, the best physical understanding that physicists have is that the wave-like behavior of particles is because of this wave of possibilities being something that is physically real. It is the wavefunction - the wave of possible quantum states - that pass through both slits in the double slit experiment, for example. 

Physicists have long tried to understand and interpret what this means. The traditional Copenhagen interpretation of quantum physics asserts that the quantum wavefunction is a physically accurate description of the quantum state prior to observation, and it is the act of observation that serves as the Heisenberg cut at which the wavefunction collapses. The concept of quantum decoherence, on the other hand, suggests that the wavefunction collapses at some other point, without requiring the act of a specific "observation." Still other approaches, such as the Many Worlds Interpretation of quantum physics do not require any wavefunction collapse.

Though the desire to really understand what happens in quantum physics is deep and important to science, it should be noted that this controversy doesn't have any real impact on physicists' ability to use this mathematical formalism to make predictions.

 

Also Known As: Wavefunction, Statefunction, Schroedinger Equation, Schroedinger Wavefunction