(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A wave function ψ is A(e^{ix}+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.

2. Relevant equations

3. The attempt at a solution

So to normalize the function, I multiplied it by its complex conjugate (A(e^{-ix}+e^{ix}) and got:

∫A^{2}[(e^{ix}+e^{-ix})(e^{-ix}+e^{ix})dx=1 From -π to π

∫2A^{2}dx=1

2A^{2}x(from -π to π)=1

2A^{2}π+2A^{2}π=1

4A^{2}π=1

A=sqrt(1/4π)

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)(e^{ix}+e^{-ix})dx From 0 to π/8

(sqrt(1/4π))∫(e^{ix}+e^{-ix})dx

(sqrt(1/4π))(ie^{ix}-ie^{-ix})

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.

Aglo6509

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