It is finally time to solve for the constant A, which is coined by the term, normalizing the wave function. Which is, the chance that the particle appear somewhere between 0 and L is the sum of all possibilities that it will appear in each specific location.

But in our situation we only need to worry the behavior within our boundary conditions so this leads us to produce

Solving for A (sub n)

Finally our solution of a normalized wave function using the Schrödinger equation of a particle in quantum state n becomes