Answer Happy

3. A particle with mass m and energy E (where (<E<V0moves in the potential: for x < L/2, V(x) = Vo for 2 > L/2. ( = { a. Solve the time-independent Schrödinger equation and derive the "quantization conditions” for the energies of even wavefunctions o(-x) = 4(x). (10 points) b. Solve the time-independent Schrödinger equation and derive the "quantization conditions" for the energies of odd wavefunctions o(-x) = -4(x). (10 points) Hint for (a) and (b): It is helpful to introduce the parameters: z=(2mE/12)/2L/2 zo = (2mV/H)2L/2 c. Show graphically that there is always at least one even solution for any value of Vo and L. (4 points) d. Find graphically the condition that V, and I must satisfy for there to be exactly 4 bound states. (7 points)