A wave function ψ is A(eix+e-ix) in the region -π<x<π and zero elsewhere. Normalize the wave function and find the probability of the particle being (a) between x=0 and x=π/8, and (b) between x=0 and x=π/4.
The Attempt at a Solution
So to normalize the function, I multiplied it by its complex conjugate (A(e-ix+eix) and got:
∫A2[(eix+e-ix)(e-ix+eix)dx=1 From -π to π
2A2x(from -π to π)=1
Now that I have the function normalized, I can find the probability the question asks for. The problem I'm having is however do you take the integral of complex numbers the same way as a real number?
The best attempt I can get is:
∫(sqrt(1/4π)(eix+e-ix)dx From 0 to π/8
Would I now just plug in 0 and π/8 and leave my answers in terms of i?
Thanks for taking the time to look at this.