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## Quantum Time Evolution: Instructor's Guide

### Main Ideas

- Time evolution of quantum systems
- Stationary states

### Students' Task

*Estimated Time: 20 min*

Students work in groups to solve for the time dependence of two quantum particles under the influence of a Hamiltonian. Students find the time dependence of the particles' states and some measurement probabilities.

### Prerequisite Knowledge

- Spin 1/2 systems
- Familiarity with how to calculate measurement probabilities
- Solutions to the Schrödinger equation
- Dirac notation

### Props/Equipment

- Tabletop Whiteboard with markers
- A handout for each student

### Activity: Introduction

Little introduction is needed, although you may want to review how to find a time-evolved state for a time-independent Hamiltonian.

### Activity: Student Conversations

### Activity: Wrap-up

The main points of this activity are addressed in the last question. Students should recognize:

- a pattern of how these calculations proceed, and should learn to recognize
- a stationary state
- that measurement probabilities of non-stationary states will be time-dependent UNLESS you measure a quantity that commutes with the Hamiltonian.