Eigenmath Manual
Quick Reference
Additional Resources
▷ Demo 1
▷ Demo 2
▷ Demo 3
▷ Demo 4

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

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

Fermion operators
▷ Anticommutation
▷ Wavefunction operator
▷ Position operator
▷ Exchange energy
▷ Energy matrix
▷ Superposition of eigenstates

How Planck calculated h and k

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

▷ Verify quantum LRL operators

▷ Rydberg unit of energy

Spontaneous emission
▷ Verify

How Einstein derived Planck's law
▷ 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

Muon decay
▷ Compute muon lifetime
▷ Verify muon decay formula (1)
▷ Verify Casimir trick

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