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.
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.
