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A wave function or wavefunction is a mathematical tool used in quantum mechanics to describe the quantum state of a particle or system of particles. It is a function typically of space or momentum or spin and possibly of time that returns the probability amplitude of a position or momentum for a subatomic particle. Mathematically, it is a function from a space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics (the Schrödinger equation) describe how the wave function evolves over time.
It is commonly applied as a property of particles relating to their waveparticle duality, where it is denoted ψ(position,time) and where  ψ  ^{2} is equal to the chance of finding the subject at a certain time and position.^{[1]} For example, in an atom with a single electron, such as hydrogen or ionized helium, the wave function of the electron provides a complete description of how the electron behaves. It can be decomposed into a series of atomic orbitals which form a basis for the possible wave functions. For atoms with more than one electron (or any system with multiple particles), the underlying space is the possible configurations of all the electrons and the wave function describes the probabilities of those configurations.
A simple wave function is that for a particle in a box. Another simple example is a free particle (or a particle in a large box), whose wave function is a sinusoidal where, in the spirit of the uncertainty principle, the momentum is known but the position is not known.
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