1. Wave functions, Energy Levels and Particle in the Box
To Review
We now have a lot of backdrop laid to start talking about more complicated topics in quantum mechanics. We eventually would like to be able to have a way to describe how an electron moves around in a hydrogen atom. However this is an extremely complex problem even for the physics who worked on the problem, a very long time ago. So they started by using a model which instead took an electron and put it in a box that it couldn’t get out of, and let it move around in that. This model is called the particle in the box model and allowed theoretical physicists to determine the methodology for calculating the exact movement of an electron in a hydrogen atom. This is where we are going to start today.

3. Particle in a Box: A Model
Look at the Blue only!
This is the wavefunction.
A)Particle in a box according to Newtonian physics. B-D) Quantum mechanical interpretation B) Particle in a box n=1 C) Particle in a box n=2 D) Particle in a box n=3.
(Blue is real component, red is the imaginary component)

4. Particle in a Box: Solutions
Solution to Schrödinger equation:
L is the length of the box.
n is the quantum number L .

5. Question 1
For the picture shown below, decide if it is a wave function or probability density. State the energy level. How many nodes are present? Draw the probability density. Do this without looking at the answer on the slides please! You won’t have those on the exam.