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Results: Quantum State Vectors

accessibility_new Kinesthetic

10 min.

Spin 1/2 with Arms

Quantum State Vectors Complex Numbers Spin 1/2 Arms Representation

Arms Sequence for Complex Numbers and Quantum States

Students, working in pairs, use their left arms to represent each component in a two-state quantum spin 1/2 system. Reinforces the idea that quantum states are complex valued vectors. Students make connections between Dirac, matrix, and Arms representation.

accessibility_new Kinesthetic

10 min.

Using Arms to Represent Overall and Relative Phase in Spin 1/2 Systems

quantum states complex numbers arms Bloch sphere relative phase overall phase Bloch sphere

Arms Sequence for Complex Numbers and Quantum States

Students, working in pairs, use the Arms representations to represent states of spin 1/2 system. Through a short series of instructor-led prompts, students explore the difference between overall phase (which does NOT distinguish quantum states) and relative phase (which does distinguish quantum states).

accessibility_new Kinesthetic

10 min.

Using Arms to Represent Time Dependence in Spin 1/2 Systems

arms quantum states time dependence

Arms Sequence for Complex Numbers and Quantum States

Students, working in pairs, use their left arms to demonstrate time evolution in spin 1/2 quantum systems.

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.
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