1. Solve the time-independent Shrodinger equation with appropriate boundary conditions for an infinite square well centered at the origin [V(x) = 0 for-a/2<x<a/2; V(x) == otherwise]. Confirm that your solution can be obtained by substitution x→x-a/2 in the results obtained in lecture notes. Calculate <x>, <x²>, <p>, <p²>, o, and op for the nth stationary state of the infinite well. Verify that the Heisenberg uncertainty principle is satisfied. Find the state that comes closest to the uncertainty limit. 2. Plot the Kronig-Penney solution over up to 4 periods for B=mavo/h²k-5 and Vo/a = 1. Find the energy at the top of the first allowed band and the energy difference of the band gap. Also show that the solution below Yn+1(x) = C[sin(Kx) + e¯ika sin(Ka)]; 0≤x≤a satisfies the Kronig-Penney model equation.

Fig: 1