Navigate to course home page

9 Atomic Wells

Keywords: Eigenstates, Wave vector, Time evolution, Periodic Systems


Highlights of the activity

  1. Nine students are selected from the class to represent the wave function of an atom, where the wave function is represented by $$\sum_{n=1}^{N} A\, e^{ikna}\; \phi (x-na) \; \; ,$$ $$k=\frac{-N\pi}{L}, … ,\frac{-2\pi}{L},0, \frac{2\pi}{L}, \frac{4\pi}{L}, … , \frac{N\pi}{L} \; \; .$$
  2. Each student will then put their arm in a particular direction to represent the value of their $e^{ika}$ term.
  3. The class is then asked to determine the wave vector of the envelope function.
  4. A second group can be selected to perform the same demonstration with a different wave vector.
  5. The energies of the eigenstates can then be compared using $$E=\alpha + 2\beta \, \cos{ka} \; \; .$$

Reasons to spend class time on the activity

Students will oftentimes have a difficult time realizing that, given the spacing of the potential wells and the number of potential wells in the system, they can formulate the eigenstates of an electron in a potential landscape with little challenging computation. This exercise is designed to help students practice looking at the graphical representation of an eigenstate and determining the wave vector of the eigenstate.


Instructor's Guide

Authors: Ethan Minot, Janet Tate, Teal Pershing
To edit this page, go here

Personal Tools