Schrdinger equation

Problem 4. The time dependent Schrodinger equation for the free particle in the 1-dimensional box ? = [0, L] is given by 12 02 2m 0x2 - ih- at W(x, t) = 0, with boundary conditions V(0,f) = 0 = V(L, t). The states were given by amb sin (a) (5 pts.) Using Euler's formula, plot the real and imaginary parts of the state wh(x, t) for times * = 0, t = 1/2 and t = 1. For the simplicity of plotting, use m = h = L =1. However, keep these constants in the equation for the remainder of the problem. (b) (5 pts.) Show that the real and imaginary parts of 1(2, () solve the wave equation 1 02 Ox2 + u(x, t) = 0, for a certain value of c with Dirichlet boundary conditions u(0, f) = 0 = u(L, t). Showing this will also require you to determine c