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

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)

Moller scattering

▹Verify Casimir trick

▹Verify formulas

▹Draw probability density

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

Notes

LEP was the Large Electron Positron collider at CERN in Geneva, Switzerland.

PEP was the Positron Electron Project collider at the Stanford Linear Accelerator Center (SLAC) in Menlo Park, California.

PETRA was the Positron Electron Tandem Ring Accelerator at DESY in Hamburg, Germany.

SPEAR was the Stanford Positron Electron Asymmetric Ring collider at SLAC.

R² is coefficient of determination, a statistic that measures the predictive accuracy of a mathematical model.

To run Eigenmath in a terminal window, download eigenmath.c and follow the build instructions. See also github.

Please send bug reports to yo73137@gmail.com

How Planck calculated

How Einstein derived Planck's law

Dirac equation

▹Verify solutions

Balmer formula

▹Compute model coefficient

Stefan-Boltzmann law

▹Calculate

Quantum electric field

▹Verify