Use variational principle to solve the particle-in-a-box problem. Assume a trial function \(x) = x³ (a³ − xb) where 'a' is the width of the box. 1- Does this function satisfy the boundary conditions associated with the particle in a box? 2- Normalize . 3- Find the optimum value of the parameter 'b' which minimizes the energy. What is the energy?