I'm reading a QM book. It first says for wave function:
"The state of a physical system (or particle) is completely specified by an entity associated with it called a wave function, Ψ , that in general depends on the spatial coordinates of the system and time. The square modulus of this wave function is the probability density for finding the system with a specified set of values for the spatial and temporal coordinates"
But later it says:
"At any given instant in time, the wave function Ψ of a particle (or an isolated system) can be expressed as a linear superposition of a complete orthonormal set of wave functions Ψn"
"$a_n = |c_n|^2$ represents the probability that the system will be found in state Ψn"
We, already, can get probabilities of system from wave function itself. What is that orthonormal wave functions thing?