16 3. The following wavefunctions (N.B. selection is dependent on the parity of the quantum number) have been proposed as solutions for a particle in an infinitely deep symmetric well with zero potential energy at walls located at -L/2 and L/2: NINI Yoda (x) = nix COS Yeven (X) = MINT sin nix where 'odd' and 'even' refer to the parity of n, i.e. if n = 1, 3, 5 ... then this is 'odd' etc. a) Sketch the first two wavefunctions. b) State the boundary conditions that apply for this well. c) Given the general solution to the Schrodinger equation for a particleina1-Dboxisgiven by : 4(x) = Aelkx + Be-ikx Show, through application of the boundary conditions, that the proposed wavefunctions are appropriate