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group Small Group Activity

10 min.

Using Tinker Toys to Represent Spin 1/2 Quantum Systems

spin 1/2 eigenstates

Arms Sequence for Complex Numbers and Quantum States

Students use Tinker Toys to represent each component in a two-state quantum spin system in all three standard bases (\(x\), \(y\), and \(z\)). Through a short series of instructor-led prompts, students explore the difference between overall phase (which does NOT change the state of the system) and relative phase (which does change the state of the system). This activity is optional in the Arms Sequence Arms Sequence for Complex Numbers and Quantum States.

group Small Group Activity

30 min.

Expectation Values for a Particle on a Ring

central forces quantum mechanics eigenstates eigenvalues hermitian operators quantum measurements degeneracy expectation values time dependence

Quantum Ring Sequence

Students calculate the expectation value of energy and angular momentum as a function of time for an initial state for a particle on a ring. This state is a linear combination of energy/angular momentum eigenstates written in bra-ket notation.

group Small Group Activity

30 min.

Superposition States for a Particle on a Ring

central forces quantum mechanics eigenstates eigenvalues quantum measurements angular momentum hermitian operators probability superposition

Quantum Ring Sequence

Students calculate probabilities for a particle on a ring whose wavefunction is not easily separated into eigenstates by inspection. To find the energy, angular momentum, and position probabilities, students perform integrations with the wavefunction or decompose the wavefunction into a superposition of eigenfunctions.

face Lecture

5 min.

Quantum Reference Sheet

face Lecture

30 min.

Time Evolution Refresher (Mini-Lecture)

schrodinger equation time dependence stationary states

Quantum Ring Sequence

The instructor gives a brief lecture about time dependence of energy eigenstates (e.g. McIntyre, 3.1). Notes for the students are attached.
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