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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