4. ( /24 pts) Consider a potential given by OO x

/ 24 pts) Consider a potential given by where Vo and L are positive constants. A particle subject to this potential has energy E such that (a) (4 pts) Sketch the system. Label regions as I, II, and III. (b) (8 pts) Use the Schrodinger equation to show that the general solution of the wave function has the form C cos(gx) + D sin(gx) 0 < < L Aekx + Bekc VIII Determine expression for the constants k and g in terms of E and Vo. (c) (6 pts) Use the boundary conditions + 00 and = 0 to show which coeffcients in and VIII are zero. (d) (6 pts) Use the boundary conditions VII(L) = "III(L) and = VIII(L) to determine a transcendental equation in terms of L, k, and g.