In the Copenhagen interpretation of quantum mechanics, the "wave function" is a fundamental concept that describes the state of a quantum system. It provides a mathematical representation of the probability amplitudes associated with different possible outcomes of a measurement.
Mathematically, the wave function is usually denoted by the Greek letter Psi (Ψ). It is a complex-valued function that depends on the coordinates of the particles in the system. In the case of a single particle, the wave function is a function of its position (Ψ(x)), while for multiple particles, it becomes a function of the positions of all the particles involved.
The wave function contains information about all possible states the system can occupy and the probabilities associated with each state. When a measurement is made on the system, the wave function collapses, and one of the possible outcomes is observed with a certain probability determined by the square of the amplitude of the wave function for that particular outcome.
According to the Copenhagen interpretation, the wave function is a mathematical tool used to calculate probabilities and make predictions about the behavior of quantum systems. It does not represent a physical reality in itself but rather provides a description of our knowledge or information about the system. The collapse of the wave function upon measurement is seen as a fundamental and non-deterministic aspect of quantum mechanics, introducing randomness into the outcomes of measurements.