Activity Links:
Central Forces on an Airtable (cfairhockey)
Visualizing Spherical Harmonics Using a Balloon (cfballoon)
Plotting Conic Sections (cfconics)
Exploring the Effective Potential (cfeffpotential)
Guessing the Legendre Polynomial Expansion of a Function (cfguessleg)
Hydrogen Wave Function Probability Densities (cfhydrogenvis)
Legendre Polynomial Series Coefficients (cflegseries)
A Hermite Polynomial (cfmbhermiteone)
Series Solutions (cfmbseriessolutions)
Trajectories in an Attractive Central Potential (cforbits)
Quantum Calculations on the Hydrogen Atom (cfqmatomgroup)
Probability of Finding an Electron Inside the Bohr Radius (cfqmbohrradius)
Particle Confined to a Ring (cfqmring)
Energy and Angular Momentum for a Particle on a Ring (cfqmringgroup)
Time Dependence for a Particle on a Ring (cfqmringgroup2)
Superposition States for a Particle on a Ring (cfqmringgroup3)
Expectation Values for a Particle on a Ring (cfqmringgroup4)
Visualization of the Spherical Harmonics (cfqmsphere)
Radial Wavefunctions (cfradialwavefunc)
Survivor Outer Space (A kinesthetic approach to introducing Center of Mass) (cfsurvivor)
Interpreting Effective Potential Plots (cfveffkin)
Velocity and Acceleration in Polar Coordinates (cfvpolar)
Linear Combinations of Spherical Harmonics (cfylmcombo)
Finding the Coefficients of a Spherical Harmonic Series (cfylmseries)
Charge density and delta functions -- SLAC Lightening Strike (coloradochargedelta)
Distinguishing Scalar and Vector Quantities Related to Electric Fields (coloradoclicker1)
Surface Current Density (coloradoclicker10)
Visualizing the Position Difference Vector 1 (Magnetic Vector Potential) (coloradoclicker11)
Direction of the Magnetic Vector Potential 1 (Infinitesimal Contribution) (coloradoclicker12)
Visualizing the Position Difference Vector 2 (Magnetic Field, Multiple Choice) (coloradoclicker13)
Direction of the Magnetic Vector Potential 2 (Arbitrary Wire) (coloradoclicker14)
Curl of the Magnetic Vector Potential (Cylindrical) (coloradoclicker15)
Curvilinear Unit Vectors and Integrals (coloradoclicker16)
Direction of the Magnetic Vector Potential 3 (Bent Wire) (coloradoclicker17)
Visualizing the Position Difference Vector 3 (Magnetic Field, Drawing) (coloradoclicker18)
Visualizing A Vector Integral (Biot-Savart Law) (coloradoclicker19)
Electric Flux Through A Cube (coloradoclicker2)
Magnetic Field and Vector Potential (coloradoclicker20)
Magnetic Field From A Small Line Segment (coloradoclicker21)
Stoke's Theorem Surface or Line Integral (coloradoclicker22)
Amperian Loop With Two Wires (coloradoclicker23)
Amperian Loop With Magnetic Field Defined Algebraically (coloradoclicker24)
Allowed Electric Fields and Potentials (coloradoclicker25)
Integrating the Magnetic Vector Potential (coloradoclicker26)
Allowed Magnetic Fields (coloradoclicker27)
Implications Of Gauss's Law (coloradoclicker3)
Choosing A Gaussian Surface For A Plane (coloradoclicker4)
Gauss's Law For A Line Of Charge (coloradoclicker5)
Visualizing Zero Divergence (coloradoclicker6)
Locating Divergence (coloradoclicker7)
Charge Density from Electric Field (coloradoclicker8)
Finding Total Charge (coloradoclicker9)
Conceptually understanding conductors (coloradoconductors)
Designing an Electric Field (coloradodesignefield)
Applying the Second Law (eeapply2ndlaw)
Two Interacting Black Body Objects (eebbobjects)
Combining Probabilities (eecombineprob)
Comparing the System and Surroundings (eecompsyssurr)
Students as molecules (eedicelab)
Temperature Change of Dissolving Salt (eedissolvesalt)
Elevator (eeelevator)
Demonstrating Extensivity in the Fairness Function (eefairextens)
Free expansion quiz (eefree_expansion)
Ice Calorimetry Lab (eeice)
Maximizing the Lagrangian (eemaxlagrange)
Finding a Chain Rule (eembchainrule)
Total Differentials on a Surface (eembdiffsurf)
Elevator Cycle (eembelevator)
PDM Legendre Transformations (eembpdmlegendretransforms)
Melting Ice Lab (eemeltingice)
Entropy of a Microcanonical Ensemble (eemicrocanonens)
Name the Experiment: Introduction (eenametheexperiment)
Name the Experiment: Changing Entropy (eenametheexperiment2)
Name the Experiment: Maxwell Relations (eenametheexperiment3)
Using $pV$ and $TS$ Plots (eepvplots)
Rubber Band Lab (eerubberband)
Analyzing a Simple Cycle Using a $pV$ Curve (eesimplecycle)
Solve for the Fairness Function (eesolvefair)
Always, Sometimes, or Never True (eesomeneverall)
Covariation in Thermal Systems (eesurfcovariation)
Quantifying Change (eesurfderiv)
Heat Capacity of Water Vapor (eesurfheatcap)
Squishability of Water Vapor (eesurfsquish)
Thermodynamic States (eesurfstates)
Partial Derivatives of Internal Energy (eesurfuderiv)
Thermodynamic Partials (eethermopartials)
Comparing Thermodynamic Properties (SWBQs) (eethermoterms)
Calculating the Internal Energy of a Diatomic Ideal Gas (eeudiatomicidealgas)
Is Work Done on or by the System? (eeworkexamples)
Visualizing Plane Waves (emplanewave)
Comparing Representations of Electromagnetic Waves (emplanewavecompare)
Visualizing Electromagnetic Plane Waves (emplanewaveem)
Scalar Plane Waves (emscalarplanewave)
Deriving Change of Variables (inchangeofvars)
Constant Lines in the U-V Plane (inconstantuvlines)
Cyclic Chain Rule (incycchainrule)
Dividing by Differentials (individingbydifferentials)
Easy and Hard Derivatives (ineasyhard)
The Isothermal Bulk Modulus (inisobulkmod)
Isowidth and Isoforce Stretchability (inisowidth)
Introducing Legendre Transforms (inlegendre)
Paramagnetism (inmagneticsusceptibility)
Naming and Classifying Thermodynamic Variables (innamingvar)
Legendre Transforms on the PDM (inpdmlegendretransforms)
Potential Energy of an Elastic System (inpotentiallab)
PDM Variables (inquantchange)
Calculating a Total Differential (intotaldiff)
Upside Down Derivatives (inupdownderiv)
Evaluating Total Differentials: "Zapping with d" (inzapd)
The Cake (mvcake)
Chain Rule (mvchain)
Chop and Add (mvchop)
The Roller Coaster (mvcoaster)
The Cone (mvcone)
Cross Product (mvcross)
The Cube (mvcube)
The Cylinder (mvcylinder)
Directional Derivatives (mvdderiv)
Partial Derivatives (mvderivs)
Double Integrals (mvdouble)
Curvilinear Volume (mvdscoord)
The Gold Mine (mvgoldmine)
The Heater Activity (mvheater)
The Heater II (mvheater2)
The Hillside (mvhillside)
The Hot Plate (mvhotplate)
Maxima & Minima (mvmaxmin)
The Park (mvpark)
Chain Rule Measurements (mvpchain)
Lines and Planes (mvplanes)
The Puddle (mvpuddle)
Resistors (mvresistors)
Surfaces (mvsurfaces)
The Tetrahedron (mvtetra)
The Triangle (mvtriangle)
The Water Table (mvwater)
Energy Diagram Analysis (osenergydiagramsim)
Guessing the Fourier Expansion of a Function (osfourierguess)
Fourier series: a piecewise periodic function (osfourierpiecewise)
LRC Lab: Harmonic Driver (osharmoniclrclab)
Products of harmonic functions and projections (osharmonicproj)
LRC Circuit: Impulse Driver (osimpulselrclab)
Initial conditions (osintialconditions)
Pendulum Lab (ospendulumlab)
Pendulum Period Calculations (Numerical Approach) (ospendulumworksheet)
Pendulum Period Calculation (Power Series) (ospendwspowerseries)
Three driving voltages (osthreesindrivers)
9 Atomic Wells (ppatoms)
Journal Club Presentations (ppjournal)
Fourier Transform of a Delta Function (ppmbdeltafourier)
Eigenvector Decomposition (ppmbeigendecomp)
Matrix Exponentials (ppmbmatrixexp)
Parseval's Identity (ppmbparseval)
The Optical and Acoustic Branches of an Infinite Diatomic Chain (ppoptacoubranches)
Coupled Oscillators and the Monoatomic Chain (P.S. Lab 1) (ppperiodiclab1)
The Diatomic Chain (P.S. Lab 2) (ppperiodiclab2)
The Periodic Finite Square Well Potential (P.S. Lab 3) (ppperiodiclab3)
Pendulum System: Single Pendulum (ppsinglepend)
Emulating Waves in a Periodic System (ppwaveemulate)
Introduction to Bra-Ket Notation (prbraket)
Visualizing Complex Two-Component Vectors (prcomplexarms)
Visualizing Complex Numbers (prcomplexnum)
Diagonalizing Matrices (prdiagmatrix)
Eigenvalues and Eigenvectors (preigenvectors)
Linear Algebra Review (prlinearalgebra)
Linear Transformations (prlineartrans)
Finding Matrix Elements (prmatrixelems)
Harmonic Oscillator Basis States (qmshobasis)
Time Evolution of Harmonic Oscillator States (qmtimesho)
System of Two Spin-1/2 Particles (qmtwospin)
Zeeman Perturbation Matrices in the Coupled Basis (qmzeemancoupled)
Coriolis and Centrifugal Accelerations (rfacc)
Cosmic Rays (rfcosmic)
Doppler Effect (rfdoppler)
Earth Hockey (rfearthhockey)
Energy-Momentum in Different Frames (rfeframes)
Earth Hockey I (rfehockey1)
Earth Hockey II (rfehockey2)
Lorentz Transformations for Electromagnetism (rfemlorentz)
Galilean Spacetime Diagrams (rfgalilean)
Length Contraction (rflength)
Linear Acceleration (rflinacc)
Mass is not Conserved (rfmass)
Rocket from the North Pole (rfnorth)
Paradoxes I (rfparadox1)
Paradoxes II (rfparadox2)
Turntable Hockey (rfthockey)
Merry-Go-Round (rfturn)
Analyzing a Spin-1/2 Interferometer (spanalyzespinhalfint)
Analyzing a Spin-1 Interferometer (spanalyzespinoneint)
The Birthday Problem (spbirthday)
Calculating 'crossed - polarizers' effect (spcrossedpolarizer)
Matrix Elements in Dirac Notation (spdiracmatrixelements)
Practice Finding Expectation Values (spexpecavg)
Expectation Value and Uncertainty (spexpectvaluncert)
Dice Rolling Lab (spfairdice)
Probabilities for Different Stern Gerlach Analyzers (sphalfanalyzer)
Probabilities in the Z-direction for a Spin-$\frac{1}{2}$ System (sphalfprob)
Infinite Square Well 1 (spinfsquarewell1)
Infinite Square Well 2 (spinfsquarewell2)
Introduction to Stern-Gerlach Simulation (spintro)
Lorentz Force and Work Done on a Rectangular Loop (splorentzforce)
Neutrino Oscillations (spneutrinos)
Describing the Sample Oven in the Stern-Gerlach Experiment Mathematically (spoven)
Projection Operators (spprojectionoperators)
Quantum Time Evolution (spqmevolution)
Superposition in Quantum Mechanics (spqmsuperposition)
Quantum Friend (spquanfriend)
Naming Quantum Operators (spquanop)
Quantum Measurement Play (spquantumplay)
Components of the Stern Gerlach Experiment (spsgexperiment)
Spins Lab 1 (spspin1)
Spins Lab 2 (spspin2)
Spins Lab 3 (spspin3)
Spins Lab 4 (spspin4)
Spin 1/2 with Arms (spspinhalfarms)
Determining how a Magnetic Field Changes a Particle's State (spspinhalfbfield)
Finding Unknown States Leaving the Oven in a Spin-$\frac{1}{2}$ System (spspinhalfunknowns)
Probabilities for Different Spin-1 Stern Gerlach Analyzers (spspinoneanalyzer)
Finding the Unknown States Leaving the Oven in a Spin-1 System (spspinoneunknowns)
Matrix Representation of Spin Operators (spspinoperators)
Quantum Postulates (spspinpostulates)
From Spin to Position (spspintoposition)
Time-dependent Spin Vector (spspinvector)
Quantum Spookiness (spspookiness)
State Formalism (spstateformalism)
Finding if $S_{x}, \; S_{y}, \; and \; S_{z}$ Commute (spsxyzcommute)
Visualizing Complex Time Dependence for Spin 1/2 System (sptimedepcomplex)
Time Evolution Introduction (sptimeevolution)
Analyzing the Probabilities of Time-Evolved States (sptimeevolvestate)
Acceleration (vcaccel)
The Cone (vccone)
Curvilinear Coordinates (vccoords)
Change of Variables (vccov)
Divergence and Curl (vccurl)
The Cylinder (vccylinder)
The Partial Derivatives Machine (vcderivmach)
Partial Derivatives (vcderivs)
Double Integrals (vcdouble)
Finding dr-vector (vcdr)
The Grid (vcgrid)
The Hill (vchill)
Climbing a Hill (vchillgrad)
Vector Line Integrals (vcline)
Potential Functions (vcmmm)
The Fishing Net (vcnet)
Which Way is North? (vcnorth)
Lines and Planes (vcplanes)
The Pretzel (vcpretzel)
Stokes' Theorem (vcstokes)
The Tetrahedron (vctetra)
The Valley (vcvalley)
Angles between Vectors (vcvectors)
The Wire (vcwire)
Partial Derivative Machine (vf1dpdm)
Acting out the Gradient (vfactinggrad)
Ampère's Law (vfampere)
Magnetic Vector Potential Due to a Spinning Charged Ring (vfaring)
Curvilinear Basis Vectors (vfbasisvectors)
Magnetic Field Continuity Across a Boundary (vfbbound)
Magnetic Field Due to a Spinning Ring of Charge (vfbring)
Acting Out Charge Densities (vfchargedensity)
Conductors (vfconductors)
Visualizing Curl (vfcurlvis)
Acting Out Current Density (vfcurrentdensity)
Surface and Volume Elements in Cylindrical and Spherical Coordinates (vfdadvcurvi)
Visualizing Divergence (vfdivergence)
Drawing Electric Field Vectors (vfdrawfield)
Drawing Equipotential Surfaces (vfdrawquadrupole)
Vector Differential (vfdrvectorcurvi)
Scalar Distance, Area, and Volume Elements (vfdsscalar)
Electric Field Continuity Across a Boundary (vfebound)
Electrostatic Energy of Discrete Charges (vfemenergy)
Electric Field Due to a Ring of Charge (vfering)
Calculation of Flux (vffluxcalculation)
The Concept of Flux (vffluxconcept)
Visualizing Electric Flux (vffluxem)
Gauss's Law (vfgauss)
Visualizing Gradient (vfgradient)
Visualizing Gradient with Surfaces (vfgradient2)
Navigating a Hill (vfhillnav)
Relaxation Technique for Solving Laplace's Equation (vflaplacerelax)
Getting Started with Maple (vfmaplestarted)
Finding Potentials from Fields - The Murder Mystery Method (vfmurdermm)
Internal Energy of the "Partial Derivative Machine" (vfpederivmach)
Approximating Functions with Power Series (vfpowerapprox)
Calculating Coefficients for a Power Series (vfpowerseriescoeff)
Pineapples and Pumpkins (vfpumpkin)
The Distance Between Two Points - Star Trek (vfstartrek)
Charged Sphere (vfsurfchargedsphere)
Equipotential Surfaces (vfsurfequisurfaces)
Isoheight on Surfaces (vfsurfheight)
Number of Paths (vfsurfnumpaths)
Work and Electric Field (vfsurfworkefield)
Theta Functions (vfthetafunc)
Total Charge (vftotalcharge)
Concept Map: VEUF (vfveuf)
Visualizing Electrostatic Potentials (vfvisv)
Potential Due to a Pair of Charges - Part 2 (vfvpoints)
Potential Due to a Pair of Charges - Part 1 (vfvpoints2)
Electrostatic Potential Due to a Ring (vfvring)
Wave Propagation in a Coaxial Cable (wvcoaxlab)
Solving the Energy Eigenvalue Equation for the Finite Well (wvfinitewell)
Boundary conditions and Fourier superposition (wvfourier)
Time Evolution of a Gaussian Wave Packet (wvgausswavepacket)
Operators and Functions (wvoperatorfunc)
Creating a Pressure-like wave in a Coaxial Cable (wvpressurewave)
Pressure Wave Simulation (wvpressurewavesim)
A Physical Model for Quantum Measurements (wvqmmeasurement)
Visualizing Reflected and Transmitted Waves (wvreftrananim)
Dispersion Relation for Waves on a String (wvstringwaves)
Time Evolution of Infinite Well Wave Functions (wvtimeinfwell)
Energy Density of Waves on a String (wvwaveenergy)
Initial Conditions (wvwaveinitialcond)