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"
and
"$a_n = |c_n|^2$ represents the probability that the system will be found in state Ψn"
What?
I'm confused.
We, already, can get probabilities of system from wave function itself. What is that orthonormal wave functions thing?