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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 Schr√∂dinger equation for a time independent Hamiltonian
  • Dirac notation

Props/Equipment

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.

Extensions


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