There needs to be some physical interpretation of the wave function and its relationship to the state of
the system. One interpretation is that the square of the wave function, ψ
2 , is proportional to the prob-
ability of fi nding the parts of the system in a specifi ed region of space. For some problems in quantum
mechanics, differential equations arise that can have solutions that are complex (contain ( 1)
1/2 i ).
In such a case, we use ψ * ψ , where ψ * is the complex conjugate of ψ . The complex conjugate of a func-
tion is the function that results when i is replaced by i . Suppose we square the function ( a ib ):