P7D.10 In the text the one-dimensional particle-in-a-box problem involves confining the particle to the range from x = 0 to x = L. This problem explores a similar situation in which the potential energy is zero between x = −L/2 andx = +L/2, and infinite elsewhere. (a) Identify the boundary conditions that apply in this case. (b) Show that cos() is a solution of the Schrödinger equation for the region with zero potential energy, find the values of k for which the boundary conditions are satisfied, and hence derive an expression for the corresponding energies. Sketch the three wavefunctions with the lowest energies. (c) Repeat the process, but this time with the trial wavefunction kx sin()