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Advanced Quantum Mechanics 2
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UoM P&AOER
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Section 5.14: Numerical calculations
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Section 6.1: Probability currents
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6
Relativistic wave equations
Last change 21/2/2012
Contents for Chapter 6
Section 6.1: Probability currents
Section 6.2: Klein-Gordon equation
Subsection 6.2.1: relativistic energy momentum relation
Subsection 6.2.2: Klein-Gordon wave equation
Subsection 6.2.3: Some simple solutions
Subsection 6.2.4: Lorentz invariance and external potentials
Subsection 6.2.5: Probability and currents
Subsection 6.2.6: Issues
Section 6.3: Dirac equation
Subsection 6.3.1: Using minimal coupling
Subsubsection 6.3.1.1: Relativistic form
Subsection 6.3.2: The Classical solution: Linearisation of the energy momentum relationship
Subsection 6.3.3: Plane wave solutions
Subsubsection 6.3.3.1: Positive energy solutions
Subsubsection 6.3.3.2: Negative energy solutions
Subsubsection 6.3.3.3: Spin?
Subsubsection 6.3.3.4: Zero rest mass: helicity basis
Subsubsection 6.3.3.5: Charge conjugation
Subsubsection 6.3.3.6: Completeness
Subsection 6.3.4: Probability
Subsection 6.3.5: Klein Paradox
Subsection 6.3.6: Lorentz transformations and external field
Subsubsection 6.3.6.1: Coupling to external fields
Subsubsection 6.3.6.2: Lorentz covariance
Subsubsection 6.3.6.3: Finite transformations
Subsection 6.3.7: Non-relativistic limit
Subsection 6.3.8: Zitterbewegung
Section 6.4: Graphene
Subsection 6.4.1: Tight binding model
Subsection 6.4.2: Dirac points--Dirac equation
Subsection 6.4.3: Klein paradox and graphene
Subsubsection 6.4.3.1: Simple potential barrier
Subsubsection 6.4.3.2: Picture of general result
Subsubsection 6.4.3.3: Experimental data
Section 6.5: Spherical symmetry
Subsection 6.5.1: Role of vector spherical harmonics
Subsection 6.5.2: Radial equations
Subsection 6.5.3: Hydrogen-like atom
Subsubsection 6.5.3.1: Relativistic approach
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Section 5.14: Numerical calculations
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Section 6.1: Probability currents
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