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-a 0 (b) A point particle of mass m moves in one dimension subject to the potential: V(x) *V(x) = 0, xs-a V V(x) = -V., -a<x<0 V(x) =V., 0<x<a V(x) = 0, a sx -V where V, is a given, real, positive constant. I II III IV -ħ? d’y(x) The time independent Schrodinger equation is +V(x)y (x) = Ey (x) ) = x. 2m 2x2 In your work below, introduce parameters k”, q?, Q and again k? for the regions I, II, III and IV respectively. You must define these parameters carefully in terms of the e, and V, given below. (i) If the particle is incident from x=-60 onto this potential with energy E = +e, (where V.>. >0), solve the time independent Schrodinger equation and write down the general solution for the wave function in each of the above four regions. State the boundary conditions which the wave function must satisfy in order to determine the various unknown coefficients which appear in your general solution, but do NOT solve for these coefficients. Note: Use R, (1,3), (L,M), T for the unknown coefficients in regions I, II, III and IV respectively. 12 marks (ii) Suppose there is a bound state of energy E =-E, (where -V <-€, <0). Again solve the time independent Schrodinger equation to find the general solutions in each of the four regions. State all the conditions necessary to determine the various unknowns which appear in your general solutions and the value of £, but do NOT solve for any of them. Note: Use (A,B), (C,D), (F,G), (H,N) for the unknown coefficients in regions I, II, III and IV respectively. 15 marks