Normalization of a wave function question

[shahramj]

A wave function (psi) equals A(exp(ix)+exp(-ix) in the region -pi<x<pi and zero elsewhere.
Normalize the wave function and find the probability of the particle being between x=0 and pi/8


Equation is : the integral of psi*(x,t)psi(x,t)=1 for normalization

 

[shahramj]

so should I integrate the (psi*)(psi) between 0 and pi/8 or first -infinity to infinity and then plug the 0 and pi/8, and how can I integrate this?
so the integral becomes: integrate(A(e^ix)+(e^-ix)) ??

 

[christianjb]

Integration need only be taken over regions where a function is non-zero.

Also- cos(x)=(e^ix+e^-ix)/2

 

[Dick]

so should I integrate the (psi*)(psi) between 0 and pi/8 or first -infinity to infinity and then plug the 0 and pi/8, and how can I integrate this?
so the integral becomes: integrate(A(e^ix)+(e^-ix)) ??

And that's not psi*psi in your 'integrate', it's just psi. psi*psi will be real.

 

[shahramj]

ok, but I didn't understand the cos(x), could you please be more specific about that, I'm new in modern physics, thanx

 

[Dick]

ok, but I didn't understand the cos(x), could you please be more specific about that, I'm new in modern physics, thanx

It's just an identity that might - or might not - come in handy. exp(ix)=cos(x)+isin(x). So exp(ix)+exp(-ix)=2*cos(x). Nothing to do with modern physics exactly.

 

[Kurdt]

You can replace e^{ix}+e^{-ix} = 2 cos(x)

Just makes the integration easier.

 

[shahramj]

Thanx, very useful hint