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# Time Dependence on a Ring

## Prerequisites

Students should be able to:

## In-class Content

- Time Dependence for a Particle Confined to a Ring (Small Group Activity, 30 minutes)
- Visualizing the Probability Density for a Particle Confined to a Ring(Maple Activity, 30 minutes)
- Superposition States for a Particle Confined to a Ring (Optional Small Group Activity, 20 minutes)
- Expectation Values for a Particle Confined to a Ring (Optional Small Group Activity, 20 minutes)

## Homework for Particle on a Ring

The following types of problems can be done as part of in-class activities and/or as homework. For examples of in-class activities, see:

Even if done in-class, it can be helpful to have follow-up homework that helps to solidify additional points (such as degeneracy or probability in wave function notation).

- (RingTable) Complete the table (EigenTableRingEmpty.pdf) which summarizes much of what you've learned about the eigenstates of the ring by filling in all the empty boxes.
- (RingFunction)
*Some quantum calculations for a particle confined to a ring.* - (RingKet)
*Some quantum calculations in Bra-ket notation for a particle confined to a ring.* - (RingCompare)
*Some quantum calculations in three different representations for a particle confined to a ring.* - (RingTimeDep)
*Some quantum calculations for a particle confined to a ring at different times.* - (RingFunc)
*Some quantum calculations on a wavefunction that is not trivially separated into energy eigenstates for a particle confined to a ring.*