Eigenmath Manual
Quick Reference
Additional Resources
▹ Demo (Demo scripts can be pasted into the Eigenmath app)

How Planck calculated h and k
▹ Demo

How Einstein derived Planck's law
▹ Demo

Muon decay
▹ Compute muon lifetime
▹ Verify density formula (Run time is about 1 minute on Safari, click through alerts on other browsers)
▹ Verify Casimir trick

Electron scattering
▹ Verify Casimir trick
▹ Verify formulas
▹ Draw probability density

Rutherford scattering
▹ Verify formulas
▹ Draw probability density

Compton scattering
▹ Verify Casimir trick (Safari recommended, click through alerts on other browsers)
▹ Verify formulas
▹ Verify lab frame formulas
▹ Draw probability density
▹ Compton scattering data from CERN LEP (R² = 0.97)

Bhabha scattering
▹ Verify Casimir trick
▹ Verify formulas
▹ Draw probability density
▹ Bhabha scattering data from SLAC SPEAR (R² = 0.99)
▹ Bhabha scattering data from DESY PETRA (R² = 0.99)

Annihilation
▹ Verify Casimir trick
▹ Verify formulas
▹ Draw probability density
▹ Annihilation data from DESY PETRA (R² = 0.98)

Muon pair production
▹ Verify Casimir trick
▹ Verify formulas
▹ Draw probability density
▹ Muon pair production data from SLAC PEP (R² = 0.87)
▹ Electroweak model (R² = 0.98)

Angular momentum
▹ Commutation relations
▹ Associated Legendre functions
▹ Spherical harmonic eigenfunctions
▹ Linear combinations

Hydrogen atom
▹ Bohr radius and Rydberg unit of energy
▹ Radial eigenfunctions
▹ Normalization
▹ Draw radial probability densities
▹ Complete solution

Electron spin
▹ Expectation values
▹ Commutation relations

Anticommutation
▹ Demo

Wavefunction operator
▹ Demo

Position operator
▹ Demo

Exchange energy
▹ Calculate

Energy matrix
▹ Calculate

Superposition of eigenstates
▹ Calculate

Dirac equation
▹ Verify

Spinors
▹ Verify

Balmer formula
▹ Compute model coefficient

Stefan-Boltzmann law
▹ Calculate

Quantum electric field
▹ Verify

Angular distance
▹ Verify

Static spherical metric
▹ Verify

Helium atom
▹ Verify

Spontaneous emission
▹ Verify

Spontaneous emission coefficients for H-α
▹ Compute coefficients
▹ Transition probabilities

Matrix elements for quantum harmonic oscillator
▹ Compute matrix elements

2d hydrogen
▹ Verify eigenfunctions
▹ Compute matrices

Quantum computing
▹ Grover search algorithm
▹ Bernstein-Vazirani algorithm
▹ Phase estimation
▹ Order finding demo
▹ 1 + 1 = 2

Feynman and Hibbs problem 2-1 (Action for free particle)
▹ Demo

Feynman and Hibbs problem 2-2 (Action for harmonic oscillator)
▹ Demo

Feynman and Hibbs problem 2-3 (Action for constant force)
▹ Demo

Feynman and Hibbs problem 3-2 (Property of free particle kernel)
▹ Demo

Feynman and Hibbs problem 3-5 (Property of free particle wave function)
▹ Demo

Feynman and Hibbs problem 3-7
▹ Demo

Feynman and Hibbs problem 3-9 (Kernel for constant force)
▹ Demo

Feynman and Hibbs problem 3-12 (Evolution of wave function)
▹ Demo

Feynman and Hibbs problem 4-1
▹ Demo

Feynman and Hibbs problem 4-2 (Schrodinger equation for charged particle)
▹ Demo