An infinite potential well with a box in the middle V = 100, the walls of the box go from -L/2 to L/2.
The Attempt at a Solution
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You don't need perturbation theory; however, I think you may get a transcendental equation or something (I don't remember exactly what the solution is like). You know how to do this if you have a uniform potential, V0, right. Well, just do it twice, once for each of the two values of V0. Then, the Schroedinger equation also tells you how to put the pieces together (i.e. it prohibits "jagged" solutions in regions of finite potential).If the box extend all through the well, the problem is just the same as for V=0. If u just have a bumb in the middle of the well, you can use perturbation theory.