Today's problem: energies of states in a crystal

So for today's problem, try to finish that by calculating E vs k for that 1-D chain of attractive delta functions and assuming phi_0 is just the g.s. for one delta function. Does that make sense?

Don't forget to graph it; that is important! And think about the energy scale. Is it positive or negative? Are the energies above or below those for the isolated atom? Is Ek real?

Also, you might want to think about the range of k. What if k is 2 pi/a ? or 3 pi / a ? Is there some limit on k or something?