Consider a particle trapped in a box with infinitely hard walls. The task is to find what is within the box, namely, between x

Consider a particle trapped in a box with infinitely hard walls. The task is to find what ψ is within the box, namely, between x = -L/2 and x = L/2.

(a) What is the time-independent Schrödinger’s equation within the box?

(b) Get the eigenvalue E_n and the normalized wave functions ψ_n of the particle.