Activities

Kinesthetic

30 min.

Time Evolution of a Quantum Particle on a Ring with Arms

Students use their arms to act out stationary and non-stationary states of a quantum particle on a ring.

Quantum Mechanics Time Evolution Arms Superposition Stationary States Non-Stationary States
Found in: Central Forces course(s) Found in: Arms Sequence for Complex Numbers and Quantum States sequence(s)

Kinesthetic

30 min.

Inner Product of Spin-1/2 System with Arms

Students use their arms to act out two spin-1/2 quantum states and their inner product.

Quantum Mechanics Arms Orthogonal States Inner Product Complex Conjugation Multiplying Complex Numbers Adding Complex Numbers.
Found in: Arms Sequence for Complex Numbers and Quantum States sequence(s)

Problem

5 min.

Dimensional Analysis of Kets

Students consider the dimensions of spin-state kets and position-basis kets.

dirac notation dimensions probability completeness relations
Found in: Completeness Relations sequence(s)

Small White Board Question

5 min.

Find the Derivative

Students are asked to "find the derivative" of a plastic surface that represents a function of two variables. This ambiguous question is designed to help them generalize their concept of functions of one variable to functions of two variables. The definition of the gradient as the slope and direction of the "steepest derivative" is introduced geometrically.

derivative partial derivative gradient

Small Group Activity

30 min.

Time Dependence for a Quantum Particle on a Ring Part 1

Practice time evolution
To calculate quantum probabilities in Dirac and Wavefunction notation
To visualize how wave wavefunctions depend on time after time evolution
To notice that not all probabilities of operators will depend on time

central forces quantum mechanics eigenstates eigenvalues angular momentum time dependence hermitian operators probability degeneracy quantum measurements
Found in: Central Forces, Theoretical Mechanics course(s) Found in: Quantum Ring Sequence sequence(s)