title, topic, keyword
Small group, whiteboard, etc
Required in-class time for activities
Leave blank to search both

Activities

In this lecture, the instructor guides a discussion about translating between bra-ket notation and wavefunction notation for quantum systems.

Small Group Activity

30 min.

Wavefunctions on a Quantum Ring
This activity lets students explore translating a wavefunction that isn't obviously made up of eigenstates at first glance into ket and matrix form. Then students explore wave functions, probabilities in a region, expectation values, and what wavefunctions can tell you about measurements of \(L_z\).

Small Group Activity

30 min.

Working with Representations on the Ring
This activity acts as a reintroduction to doing quantum calculations while also introducing the matrix representation on the ring, allowing students to discover how to index and form a column vector representing the given quantum state. In addition, this activity introduces degenerate measurements on the quantum ring and examines the state after measuring both degenerate and non-degenerate eigenvalues for the state.

Small Group Activity

30 min.

Superposition States for a Particle on a Ring
Students calculate probabilities for a particle on a ring whose wavefunction is not easily separated into eigenstates by inspection. To find the energy, angular momentum, and position probabilities, students perform integrations with the wavefunction or decompose the wavefunction into a superposition of eigenfunctions.

Small White Board Question

5 min.

Normalization of the Gaussian for Wavefunctions
Students find a wavefunction that corresponds to a Gaussian probability density.
  • Found in: Periodic Systems course(s) Found in: Fourier Transforms and Wave Packets sequence(s)