face Lecture

5 min.

Unit Learning Outcomes: Classical Mechanics Orbits

Central Forces 2023 This handout lists Motivating Questions, Key Activities/Problems, Unit Learning Outcomes, and an Equation Sheet for a Unit on Classical Mechanics Orbits. It can be used both to introduce the unit and, even better, for review.

computer Mathematica Activity

30 min.

Using Technology to Visualize Potentials

Static Fields 2023 (6 years)

electrostatic potential visualization

Begin by prompting the students to brainstorm different ways to represent a three dimensional scalar field on a 2-D surface (like their paper or a whiteboard). The students use a pre-made Sage code or a Mathematica worksheet to visualize the electrostatic potential of several distributions of charges. The computer algebra systems demonstrate several different ways of plotting the potential.

group Small Group Activity

30 min.

Energy radiated from one oscillator

Contemporary Challenges 2021 (4 years)

blackbody radiation

This lecture is one step in motivating the form of the Planck distribution.

assignment_ind Small White Board Question

5 min.

Angular Momentum

Central Forces 2023

group Small Group Activity

5 min.

Spherical Harmonics

Central Forces 2023 (4 years)

computer Computer Simulation

30 min.

Blackbody PhET

Contemporary Challenges 2021 (4 years)

blackbody

Students use a PhET to explore properties of the Planck distribution.

assignment_ind Small White Board Question

5 min.

Normalization of the Gaussian for Wavefunctions

Periodic Systems 2022

Fourier Transforms and Wave Packets

Students find a wavefunction that corresponds to a Gaussian probability density.

face Lecture

5 min.

Wavelength of peak intensity

Contemporary Challenges 2021 (3 years)

Wein's displacement law blackbody radiation

This very short lecture introduces Wein's displacement law.

group Small Group Activity

30 min.

Name the experiment (changing entropy)

Energy and Entropy 2021 (2 years)

thermodynamics entropy experiment derivative first law

Students are placed into small groups and asked to create an experimental setup they can use to measure the partial derivative they are given, in which entropy changes.

assignment_ind Small White Board Question

10 min.

Vector Differential--Rectangular

Vector Calculus II 23 (10 years)

vector differential rectangular coordinates math

Integration Sequence

In this introductory lecture/SWBQ, students are given a picture as a guide. They then write down an algebraic expression for the vector differential in rectangular coordinates for coordinate equals constant paths.

This activity can be done as a mini-lecture/SWBQ as an introduction to Vector Differential--Curvilinear where students find the vector differential in cylindrical and spherical coordinates..

group Small Group Activity

30 min.

Hydrogen emission

Contemporary Challenges 2021 (5 years)

hydrogen atom photon energy

In this activity students work out energy level transitions in hydrogen that lead to visible light.

group Small Group Activity

10 min.

Sequential Stern-Gerlach Experiments

Quantum Fundamentals 2023 (3 years)

assignment_ind Small White Board Question

10 min.

Electrostatic Potential Due to a Point Charge

Static Fields 2023 (2 years)

Warm-Up

Ring Cycle Sequence

assignment_ind Small White Board Question

5 min.

Newton's 2nd Law SWBQ

Central Forces 2023 (2 years)

group Small Group Activity

30 min.

Expectation Values for a Particle on a Ring

Central Forces 2023 (3 years)

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

5 min.

Fourier Transform of the Delta Function

Periodic Systems 2022

Fourier Transforms and Wave Packets

Students calculate the Fourier transform of the Dirac delta function.

group Small Group Activity

10 min.

Guess the Fourier Series from a Graph

Oscillations and Waves 2023 (2 years) The students are shown the graph of a function that is a superposition of three harmonic functions and asked to guess the harmonic terms of the Fourier series. Students then use prewritten Sage code to verify the coefficients from their guess. The program allows the students to enter functions of their own choice as well as the one that is preset.

group Small Group Activity

10 min.

Generalized Leibniz Notation

Static Fields 2023 (6 years) This short small group activity introduces students to the Leibniz notation used for partial derivatives in thermodynamics; unlike standard Leibniz notation, this notation explicitly specifies constant variables. Students are guided in linking the variables from a contextless Leibniz-notation partial derivative to their proper variable categories.

group Small Group Activity

5 min.

Fourier Transform of a Plane Wave

Periodic Systems 2022

Fourier Transforms and Wave Packets

computer Mathematica Activity

30 min.

Visualization of Quantum Probabilities for the Hydrogen Atom

Central Forces 2023 (3 years) Students use Mathematica to visualize the probability density distribution for the hydrogen atom orbitals with the option to vary the values of \(n\), \(\ell\), and \(m\).