Im new to quantum mechanics and prof. James Binney writes the probability amplitude of going through two paths s and t, is the mod square of A(s)+A(t). Then he writes this as The mod square of A(s)+ mod square of A(t) + A(s)A(t)* + A(t)A(s). Why is it expanded like this? Could someone please prove this to me. Also he further confused me by rewriting this as mod square of A(t) + mod square of A(s) + twice the real part of A(s)A(t)*. Can you please explain this to me too.