Time Evolution Introduction
Highlights of the activity
- Students practice simple probability calculations for a 2-level system
- Students 'discover' that some states have time independent probabilities and others oscillate
- Students build meaning of stationary states
Reasons to spend class time on the activity
Students need practice with simple time-dependent calculations early on because the Schrodinger equation is hard for them at this stage in the course. This activity also allows them to make meaning of time-independent vs. time dependent probabilities. When we give something a name like 'stationary state' often the students just parrot it back to us without really thinking about what it means. When given the opportunity to discover on their own that when you start in 'special' states the probability of finding them there some time later can be time-independent (despite a time-dependent system), then they find meaning in it themselves. I allowed the students to come up with their own name, and 'static', 'constant', and similar words were offered, so when I gave them the conventional name of 'stationary' they seemed to be quite satisfied that this was an appropriate name.