Every physically-realizable state of the system is described in quantum mechanics by a state function \(\psi\) that contains all accessible physical information about the system in that state.
The properties of a quantum mechanical system are determined by a wavefunction Ψ(r,t) that depends upon the spatial coordinates of the system and time, \(r\) and \(t\). For a single particle system, r is the set of coordinates of that particle \(r = (x_1, y_1, z_1)\). For more than one particle, \(r\) is used to represent the complete set of coordinates \(r = (x_1, y_1, z_1, x_2, y_2, z_2,\dots x_n, y_n, z_n)\). Since the state of a system is defined by its properties, \(\Psi\) specifies or identifies the state and sometimes is called the state function rather than the wavefunction.