Normalize a wavefunction: how do we normalize Ψ= x(a-x)?

[minhajoooo]

This is a little beginner level, but how do we normalize Ψ= x(a-x). I do not understand how separate the a from the equation.

 

[topsquark]

This is a little beginner level, but how do we normalize Ψ= x(a-x). I do not understand how separate the a from the equation.

In general, set
$\psi (x) = A ( x( a - x) )$

Then
$1 = \int_a^b \psi ^*(x) \psi (x) \, dx$

(In general A can be complex, but usually we can make it real.)

You can do this and keep the a. The only way to get rid of that is if you have a boundary condition you need to fill, and you didn't give one.

-Dan