What is a wave function?

A wave function is a mathematical tool to represent a physical system. It is usually denoted by the letter psi. It is usually complex, meaning- it has a real part and an imaginary part. It is usually a function of coordinate and time. If it is only a function of coordinate, the wave function is independent of time. A physical system is completely described quantum mechanically if its amplitude and phase at any time are known. Therefore, a wave function should consist of these two information - an amplitude and the phase. Once a well-defined wave function is assigned to a physical system, a complete information related to the system can be drawn easily. For example, the modulus squared of the wave function gives the probability density - meaning the probability of finding a particle per unit volume. If this quantity is integrated in the overall space, the result will be '1', which means that the particle is somewhere in that space. A wave function is the fundamental tool for a quantum physicists ! NO wave function -NO Qunatum Physics !