# 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* = |*V*_{0}| 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.

# Table of Contents

## Sections

- Section 11.1: Finite Potential Energy Wells: Qualitative.
- Section 11.2: Finite Potential Energy Wells: Quantitative.
- Section 11.3: Exploring the Finite Well by Changing Width.
- Section 11.4: Exploring Two Finite Wells.
- Section 11.5: Finite and Periodic Lattices.
- Section 11.6: Exploring Finite Lattices by Adding Defects.
- Section 11.7: Exploring Periodic Potentials by Changing Well Separation.
- Section 11.8: Asymmetric Infinite and Finite Square Wells.
- Section 11.9: Exploring Asymmetric Infinite Square Wells.
- Section 11.10: Exploring Wells with an Added Symmetric Potential.
- Section 11.11: Exploring Many Steps in Infinite and Finite Wells.

## 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.