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# Time Dependence for a Particle on a Ring

**Keywords:**Central Forces, Quantum Mechanics, Eigenstates, Eigenvalues, Angular Momentum, Time Dependence, Hermitian Operators, Probabilty, Degeneracy, Quantum Measurements, Small Group Activity

### Highlights of the activity

- This small group activity is designed to help students work out time dependent solutions for a particle on a ring.
- Students work in small groups with linear combinations of eigenstates of a quantum particle confined to a ring and calculate the probability for angular momentum, energy, and position as function of time.
- The whole class wrap-up discussion includes group presentations, allowing students to recognize time evolution of non-trivial quantum states in a variety of representations.

### Reasons to spend class time on the activity

In this activity, students lean how to find probabilities as function of time and to discuss what is required for a measurement probability to depend upon time.

### Reflections

### Instructor's Guide

### Student Handouts

**Authors:**Corinne Manogue, Kerry Browne, Elizabeth Gire, Mary Bridget Kustusch, David McIntyre

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