Activities
- How to translate a complicated wavefunction into eigenstates.
- Refresher on how to find expectation values and probabilities in a region.
- How to use the symmetry of the wavefunction to tell you something about measurements.
In this lecture, the instructor guides a discussion about translating between bra-ket notation and wavefunction notation for quantum systems.
Students use the completeness relation for the position basis to re-express expressions in bra/ket notation in wavefunction notation.
- How to form a state as a column vector in matrix representation.
- How to do probability calculations on all three representations used for quantum systems in PH426.
- How to find probabilities for and the resultant state after measuring degenerate eigenvalues.
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.
Students find a wavefunction that corresponds to a Gaussian probability density.