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

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