The Periodic Finite Square Well Potential (P.S. Lab 3)

Highlights of the activity

1. Students are placed in small groups and will use the “Electron States in a 1-Dimensional Lattice” program to model a single electron in a periodic array of square well potentials.
2. The groups will convince themselves that the program is correctly simulating periodic potential wells by finding the eigenenergies of a single potential well system and checking one or more values using the energy eigenvalue equation.
3. Each group will then add more potential wells to the quantum system and answer several questions about key differences from the single well system.
4. The class will investigate how changing certain parameters of the system (potential well depth, width, spacing, etc) will change the energy eigenvalues for the system.
5. Students will explore how increasing the number of potential wells affects the density of states for the electron in the periodic landscape.

Reasons to spend class time on the activity

This experiment offers students with a good introduction into many-well periodic potentials. Typically, students have only extensively analyzed a single-well potential system at this point; this experiment helps guide students in finding the important physical differences between a single-well system and a many-well system. Students will also have the opportunity to cross-check that the experimental tool they are using properly emulates the results predicted in the theory; this is always an important practice for a physicist utilizing simulations for more advanced modeling.

This experiment will also have students changing various parameters of the potential wells, including depth, width, number of wells, and separation distance, to see how the energy levels in the system will change. Students will investigate how making these changes will change the density of states in the system, the number of bound energy levels, and more. The observations made can also be expanded to a discussion considering a system with a large amount of wells ($\sim 10^{23}$).

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Student Handouts

ppperiodiclab3hand.doc