• Time evolution of quantum systems
• Stationary states

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.

• Spin 1/2 systems
• Familiarity with how to calculate measurement probabilities
• Solutions to the Schrödinger equation for a time independent Hamiltonian
• Dirac notation

• Tabletop Whiteboard with markers
• A handout for each student

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

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.