Welcome to Quantum Dynamics in One Dimension. In this Calculus II honors project, we will look at
- the Schrödinger equation\[i\hbar \frac{\partial}{\partial t} \psi(x,t) = H \psi(x,t) .\]
- a particle in a box.
- quantum tunneling.
- expectation values \(\langle \psi \mid X \mid \psi \rangle\).
- the quantum harmonic oscillator.
We will approach these topics using standard tools from calculus, including improper integration, series, and some differential equations. I believe the content of this project is within reach for all of you, it will require you to think. Not all the covered material will be results or techniques you have previously seen, so some assignments may seem daunting. That being said, I will do my best to guide you through the material at a comfortable pace.
Assignments and Deliverables
This honors project will be based on a few problem sets. I strongly encourage you to work together on these, but working independently is fine. In either case, please submit your own work. We will meet semi-regularly to discuss your solutions and any questions.
You will also prepare slides and give a final talk on a topic from these assignments.
Materials
- HP01: Introduction to the Schrödinger Equation
To add...
- Lecture: States, Evolutions, and Some History
After introducing the Heisenberg and Schrödinger pictures, we broke down the data of a quantum mechanical system. Along the way, we saw \(L^2\)-space, Born's rule, and the Schrödinger equation for a particle in one dimension.