6. An one-dimensional potential V is equal to zero for a

6. An one-dimensional potential V is equal to zero for a < X < a, and equal to infinite for X 2 a and X a. a) Draw the potential schematically. (l pt) b) What are the energy and wavefunction of the ground state and first excited state? (4 pts) c) In the second half of this problem, the potential in the range of a < X < a is changed to V = a(x) where a is a positive number. What are the boundary conditions at X = a and X = O? (3 pts) d) Please show that the first excited state you found in b) is not affected by the potential. (2 pts)