Chapter 11: Finite Square Well and Other Piecewise-constant Wells


Having studied the infinite square well, in which V = 0 inside the well and V = ∞ outside the well, we now look at the bound-state solutions to other wells, both infinite and finite. The wells we will consider can be described as piecewise constant: V is a constant over a finite region of space, but can change from one region to another. We begin with the finite square well (we studied scattering-state solutions to the finite well in Section 9.6 where V = |V0| inside the well and V = 0 outside the well. Solutions are calculated by piecing together the parts of the energy eigenfunction in the two regions outside the well and the one region inside the well.