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

## Introduction

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.

## Problems

• Problem 11.1:  Characterize the finite wells by width and depth.
• Problem 11.2:  Determine the number of bound states from the transcendental equations.
• Problem 11.3:  Determine the energy bands and gaps for a periodic potential.
• Problem 11.4:  Determine the number of finite wells.
• Problem 11.5:  Determine the unknown addition to these finite wells.
• Problem 11.6:  Determining the properties of half wells.