Gas Physics Introduction
Chapter 1:Energy Distribution Evolution
Energy Diffusion from Mono-energetic of a Three Dimensional Gas
Rotating Gas in a 3D Toroid
Gas Velocity Equilibration 2D
Gas Velocity Equilibration 3D
Circulating Gas in a Wind Tunnel
Density Modulated Rotating Gas in a 3D Toroid
Position Diffusion (Mixing) of a Three Dimensional Gas
Energy Distribution 3D with MathJax Equations and Embedded Canvases
Gas Energy Distributions 2D
Rigid Rotors Energy Distribution 2D
1D Gas Energy and Momentum Distribution
Rotor Energies 2D
Rotor Energies 3D
H2O Energies 3D
CO2 Energies 3D
2D Rigid Arrays with Rotation and Translation
3D Rigid Arrays with Rotation and Translation
Gas Energy Distributions 1D, 2D, 3D
Chapter 2:Particle Scattering Effects

Inelastic Collision Conversion to Internal Energy Brownian Motion Animation 2D Using Hard Sphere Scattering Large Disc Kinetics 2D Condensation of a Gas on a 2D Solid Maxwell's Demon Energy Seperator 2D Minimize Final Energy 2D and 3D Gas Diffusion 2D Gas Expansion 2D Linear Gas Expansion 2D Constant Pressure Gas Expansion 2D Circular Gas Explosion 2D Circular MagnetoCaloric Effect 2D Convection Loops in a Numerical Gas Chapter 3: Gas Energy Equipartition Energy Equipartition of a Two Dimensional Gas with Two Different Masses Energy Equipartition of a Three Dimensional Gas with Two Different Masses Gas Energy Equipartition 3D

Inelastic Collision Conversion to Internal Energy Brownian Motion Animation 2D Using Hard Sphere Scattering Large Disc Kinetics 2D Condensation of a Gas on a 2D Solid Maxwell's Demon Energy Seperator 2D Minimize Final Energy 2D and 3D Gas Diffusion 2D Gas Expansion 2D Linear Gas Expansion 2D Constant Pressure Gas Expansion 2D Circular Gas Explosion 2D Circular MagnetoCaloric Effect 2D Convection Loops in a Numerical Gas Chapter 3: Gas Energy Equipartition Energy Equipartition of a Two Dimensional Gas with Two Different Masses Energy Equipartition of a Three Dimensional Gas with Two Different Masses Gas Energy Equipartition 3D

Photoelectric Effect
Alpha Particle Emission from a Large Nucleus 2D
Black Body Emission from Charged Harmonic Oscillators
Quantum Animation of Energy Band Gap 1D
Animation of Quantum Wave Packets in a pn Junction 1D
Quantum Mirror Focusing by Iterating the Schrodinger Equation
Quantum Lens Focusing by Iterating the Schrodinger Equation
Quantum Two Mirror Resonator by Iterating the Schrodinger Equation
Entangled Quantum Object Propagation in a Parabolic Potential
Classic and Quantum Object Propagation in a Parabolic Potential
Accurate Wave Packet Propagation in a Parabolic Potential
Comparison of Quantum to Classical Physics 1D-Time Dependent
Accurate Wave Packet Propagation in a Swaged Potential
Series Solution of Wave Packet Propagation in a Infinite Square Potential
Propagation of a Wave Packet in a Parabolic Potential
Propagation of a 2D Wave Packet in a 2D Parabolic Potential
Propagation of an Asymmetric Shaped Wave Packet in a 2D Parabolic Potential
Two Slit Diffraction by Iterating the Schrodinger Equation
Two Potential Slit Diffraction by Iterating the Schrodinger Equation
Propagation of an Electron Wave Packet in an Infinite Square Well (Series Solution)
Propagation of a Free Wave Packet (Series Solution)
Series and Algebraic Solutions for Propagation of a Wave Packet in a Parabolic Potential
Comparison of Quantum to Classical Physics 1D-Time Independent Mexican Hat
Stationary Quantum States of a Finite Square Potential Well
Various Wave Packet Motion in a Finite Square Potential Well
Various Wave Packet Motion in a Swaged Potential Well
Comparison of Quantum to Classical Physics 1D-Time Independent Cosine/Parabola
Electromagnetic Modes of a 2D Cavity
Black Body Radiation Experiment and Theory
Emission of the Inner Walls of a Black Body Cavity
Multiple Slit Diffraction
Statistics of Indistinguishable Dice or Particles
Quantum Field Collapse Visualization
Matrix Operations and Eigenmodes

Tumbling Block on Inclined Plane New
Roller on Inclined Plane
Sliding Block on Inclined Plane
Classic Objects Motion 1D
Generation of Curve for Fastest Time between Two Points
Curve for Fastest Time between Two Points
Bead Sliding On a Stiff Wire
Sound Wave in Two Solid Media
Mechanical Properties of a 2D Numerically Modeled Lattice
Vibrating Reed Numerical Model 2D
Laminar Flow of a Fluid in a 2D Bearing
Animation of a Fountain 2D
Gravity Leveling of a 2D Liquid
Longitudinal and Shear Wave Sound Speed in a 2D Lattice
Mechanical Properties of a 2D Numerically Modeled Lattice
Vibration Frequencies of a 2D Numerically Modeled Lattice
Damped Harmonic Oscillator
Motion and Modes of a Particle in a Mexican Hat Potential
Forced Oscillator
Roller Bearing
Cam and Roller Follower
Simple Hybrid Gear Train
Ratchet Animation
Child's Swing Height Increase Mechanics
Roller Chain Animation
Elasticity of 3D Gas Driving a Piston
Free to Forced Harmonic Oscillator Transition
Physics of Mounting a Tire on a Rim
Physics of a Pendulum Clock Escapement
Physics of a Gas Pressure Gauge

Physics of a Gas Pressure Gauge
Ion Drift in Neutral Particle Sea
Diffusion Equation Solved by Finite Difference Method
Linear Particle Diffusion
Heat Flow 1D with Time Dependent Boundary
Solid Cube in Liquid Column
Drag on a Large Sphere Due to a Digital Gas
Animation of a Gas Centrifuge
Laminar Flow of a Gas in an Annular Space
Laminar Flow of a Fluid in a 2D Bearing
Incompressible Fluid Flow through a Constriction
Fluid Flow Due To Pressure Gradients

Parallel Resistors
Gas Discharge Animation
Oscilloscope Animation
Permanent Magnet in Solenoid
Cross Product of Two Vectors
Magnetic Braking with Cylindrical Geometry
Stopping a Falling Magnet by Eddy Currents
Magnetic Brake
Magnetic Field of a Long Solenoid Coil
Light Propagation in a Transparent Dielectric Material
Dipole Array Animations
Angular Distribution of Emission of Arrays of Excited Dipoles
Geometric Derivation of Snell's Refraction Angle Law
Electromagnetic (EM) Wave Response to a Row of Dipoles
Electromagnetic (EM) Wave Response to a Single Dipole
Optics of a Transparent Plate by Iterating the Maxwell Wave Equation
Diffraction by Iterating the Maxwell or Schrodinger Wave Equations
Lens Focusing by Iterating the Maxwell or Schrodinger Wave Equations
Optical Wave Packet Propagation by Finite Difference Matrix 1D
Potential(x,y) Using Laplace's Equation Div(gradV)=0 with Variable Boundary Geometry
Potential(x,y) Using Laplace's Equation Div(epsilon*gradV)=0
Laplace's Equation Div(gradV)=0 with Mixed BCs
Potential(x,y) for Surface Electrodes with Dielectric Slab
Dipolar Media Field Plots
LCR Oscillator Animation
Beam Trajectory of a Moving Laser
Beam Trajectory in a Square Ring Laser
Doppler Effect
Converting Magnetic Forces to Electric Forces
Converting Permanent Magnet Orbital Moments to Solenoid Currents
Electron Beam Collimation by Axial Magnetic Field
Electron Buncher for Klystron
Charged Particle Spatial and Speed Bunching
Electrical Conduction-Particle Picture
Electromagnetic Bell
Triode Vacuum Tube

E=mc^2 and Mexican Jumping Bean
Radar Pulse Return Time Interval
Experiment to Determine Gamma
Current Loop with a Rotating Test Particle
Moving Fabry-Perot Interferometer
Space Time Invariant Intervals of a Moving Clock
Relativity Transformations by Requiring Simulataneity
Accelerated Space Trip Clock Times and Rates
Minguzzi Invariant Inertial Frame Time
Accelerated Space Trip with Light Pulse Signaling

Solar Power Generation
Planet Formation
Illumination of Planets
Change of Orbit due to Asteroid Impact
Earth Time Zones
Day Lengths
Astronomical Aberration
Kepler Planetary and Sun Orbits
Model of Ocean Tides
Gravity Course Iteration
Spacecraft Speed Assistance by Gravity
Hohmann Transfer from One Circcular Orbit to Another
Star Distances Using the Parallax Method

Light Rays in a Transparent Isosceles Prism
Light Ray in a Series of Wedges of Various Index of Refraction
Snells Law of Refraction
Refraction Due to Dipoles in Two Media
Refraction and Reflection Two Media
Animation of Concave Mirror Reflection
Animation of Convex Lens Refraction
Prism Refraction-Wave Picture
Thick Lens Ray Trace
Monochromator (Czerny-Turner Type)
Wavelets from Concave Mirror>
Thick Lens Focusing

Acoustic Wave with Built-in Pressure
Acoustic Waves in 2D Numerically Modeled Solid
Wave 1D on a Linear Array
Waves on Discrete Model of Vibrating String
Linear Acoustic Wave in a 3D Gas
Spherical Acoustic Wave in a 3D Gas
Laterally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces
Longitudinally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces

Hover over the menu bar to pick a physics animation.

This is just a warmup for solutions of the eigenmodes of the one dimensional Schrodinger equation, It includes all the standard square matrix functions like multiplication, determinant, and inversion. The learner who wants to use these function for themselves is welcome to hit F12 on any Windows computer and copy them into their own Javascript program. Or just change the values of the list a or matrix m in the reSet function in this program and re-run the program by hitting F5. Note that the only matrices cosidered here are square (nxn) matrices. The program culminates with solutions for eigenvalues and eigenvalues of a 4x4 matrix but the functions available could do the same for much larger matrices. In physics second order differential equations are extremely common. These can be solved approximately by forming what is called a tridiagonal matrix where the only non-zero elements are the diagonal ones and the two next to diagonal ones. Often the neighboring elements are constants which makes the problem even simpler, for exanple

`( (d1, b, 0, 0, 0), (b, d2, b, 0, 0), (0, b, d3, b,0), (0, 0, b, d4,b), (0, 0, 0, b,d5))((v1), (v2), (v3), (v4), (v5))=lambda((v1), (v2), (v3), (v4), (v5)) `

where `lambda` is the eigenvalue and the `v` vector is the eigenvector of the matrix on the left. Another use of this tridiagonal matrix is to solve for the values v given its initial conditions. This can be done by using Newton's Method as suggested below. In the equations below, f(v) is the functional part of the diagonal of the matrix.
`F'(v) = tridiag (1/(∆x_2) , −2/(∆x_2) + f(x_i) , 1/(∆x_2))`

`F(v_k)=F(v_k)+F'(v_k)(v-v_k)`

`v-v_k=-(Inverse)(F')*F(v_k)`