# Why don't we need to normalize wavefunction to find probability distribution?

Consider an unormalized wavefunction of a rotor at $t = 0$, a combination of $n=0$ and $n=2$ states:

$$\psi(\phi) = 3 - 2 \cos (2\phi).$$

Find the probability distribution in angle.

The book simply takes probability as

$$\lvert\psi(\phi)\rvert^2 = \lvert 3 - 2\cos(2\phi)\rvert^2 = 9 + 4\cos^2(2\phi) - 12\cos(2\phi).$$

I have found the normalized wavefunction to be:

$$\psi(\phi) = \frac{3}{\sqrt {11}}\lvert 0\rangle - \frac{2}{\sqrt {22}}\lvert 2\rangle.$$

Do I use probability as $\left\lvert\frac{3}{\sqrt {11}} - \frac{2}{\sqrt {22}}\cos(2\phi)\right\rvert^2$ ? or the one in the book?

• Probabilities must add up to 1 – Floris Apr 22 '14 at 3:33
• which one do i use? – user44840 Apr 22 '14 at 4:27