Maths for (Games) Programmers Section 8 - Multivector Quantum Mechanicse

Introduction
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
Observables
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
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
Introduction
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
Web Source: www.iancgbell.clara.net/maths or www.bigfoot.com/~iancgbell/maths
Latest Edit: 01 Oct 2007.