Sierpinski (<1K)Maths for (Games) Programmers
Section 8 - Multivector Quantum Mechanicse

          Notational issues

Quantum Computers
    Quantum Bits
          Superposition     Quantum Register     Multivector Representation of a Quantum Register     Quantum Cryptograhy     Welsh-Hadamard Operator     Grover's Algorithm

Multivector Quantum Mechanical Algebras
    Quantum States
          Kets and Ketvectors     Pensities     Pensity Superpositions
          Linear Operators     Eigenkets and Eigenpensities     Probabilities     1-Observables     Uncertainty Principle     k-Observables     k-Urbservables     Position N-observable     Spin Observable     Displacement Operators     Momentum N-urbservable     Hamiltionian     Angular Momentum ½N(N-1)-urbservable     Electron Orbits
    Complex Matrix Representation
    Scalar Pensity as boolean property
          Bohm Quantum Potential
    <0;3> pensity as qubit
          Pauli Algebra        Moving into Â4.1

Multiparticle Algebras
          Multiparticle Systems     Example: Hydrogen Molecule Ground State
    Einstein-Podolsky-Rosen Paradox
          Bell's Inequality     Impossibility of FTL quantum signalling
    Multiple 4D Qubits
    Multiple 5D Qubits
          Fermionic Correlations     Bosonic Correlations     Bell States
    Quantum Teleportation

The Dirac Particle
    The 4D Dirac Equation
          The Free Dirac Equation     The Dirac Equation     Dirac Algebra     Dirac Conjugation as Clifford Conjugation     The Dirac-Hestenes Equation
    4D Dirac-Hestenes Solutions
          Particle as spinning frame field     Simple solutions     Zitterbewebung     Hydrogen Atom
    The 5D Particle
          Geometric Interpretation of the Primary Idempotent     The 5D Particle Ket     5D Dirac Particle Pensity
    Dirac Observables
          DeBroglie Observable     Probability Current     Quantum Spin Vector     Nullcurrent     Moment Density
    5D Idealised Dirac-Hestenes Equation
          Hydrogen Atom
    Multiple Dirac Particles
          Independant Particles

Generalised 5D Dirac Particle
          Further Idempotents     Simple Solutions     Grade based consequences     Almeida e0* Approach
    Beyond the Dirac Equation

References/Source Material for Multivector Quantum Mechanics

Glossary   Contents   Author
Copyright (c) Ian C G Bell 1998
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Latest Edit: 01 Oct 2007.