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 ½
N
(
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
Â
4.1
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
   
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
e
0
*
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
.