Quantum Mechanics determining the normalized constant of a particle

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tryingtolearn1
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Homework Statement
Determining the normalization constant
Relevant Equations
Normalization
In my book it has the following example,

A particle confined to the surface of a sphere is in the state

$$\Psi(\theta, \phi)= \Bigg\{^{N(\frac{\pi^2}{4}-\theta^2), \ 0 < \theta < \frac{\pi}{2}}_{0, \ \frac{\pi}{2} < \theta < \pi}$$

and they determined the normalization constant for ##N## which is $$N = \frac{1}{\sqrt{\frac{\pi^5}{8}+2\pi^3 - 24\pi^2 + 48\pi}}$$

but they never provided an example on how it was determined?
 
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tryingtolearn1 said:
but they never provided an example on how it was determined?
Given you are studying QM they probably assumed you knew how to integrate a function over a sphere.
 
PeroK said:
Given you are studying QM they probably assumed you knew how to integrate a function over a sphere.
Oh okay gotcha it never crossed my mind for some reason to integrate over a sphere especially when the the question explicitly says spheres -__-. been a long day. Thanks!
 
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