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Advanced Quantum Mechanics 2
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UoM P&AOER
To be used in future
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Section 3.1: Why symmetries?
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3
Symmetries
Last change 4/2/2012
Contents for Chapter 3
Section 3.1: Why symmetries?
Subsection 3.1.1: Linearity
Section 3.2: Examples of Symmetries
Subsection 3.2.1: Translational invariance
Subsubsection 3.2.1.1: Time translations
Subsection 3.2.2: Rotational invariance
Subsection 3.2.3: Galilean invariance
Subsection 3.2.4: Discrete symmetries
Subsubsection 3.2.4.1: Space inversion/parity
Subsubsection 3.2.4.2: Time reversal
Subsubsection 3.2.4.3: Space inversion without momentum inversion
Subsection 3.2.5: Lorentz and Poincaré invariance
Subsubsection 3.2.5.1: Boosts
Subsubsection 3.2.5.2: Full Lorentz symmetry
Subsubsection 3.2.5.3: Poincaré invariance
Subsection 3.2.6: Active and passive view of transformations
Section 3.3: Consequences for Quantum Mechanics
Subsection 3.3.1: Role of symmetry
Subsection 3.3.2: Active and passive view
Subsection 3.3.3: Symmetry generators
Subsubsection 3.3.3.1: Translations: momentum
Subsection 3.3.4: Discrete symmetries
Subsubsection 3.3.4.1: Space inversion
Subsubsection 3.3.4.2: Time reversal
Subsection 3.3.5: Simultaneous diagonalisation of operators
Subsection 3.3.6: Lorentz Boosts
Section 3.4: Unitary operators
Subsection 3.4.1: Exponent of generators
Subsection 3.4.2: Unitarity
Subsubsection 3.4.2.1: Unitarity of the transformation operators
Subsection 3.4.3: Translation in space
Subsection 3.4.4: Translation in time
Subsection 3.4.5: Rotations
Subsubsection 3.4.5.1: Euler angles
Subsubsection 3.4.5.2: Representation matrices
Subsubsection 3.4.5.3: Angular momentum states and ladder operators
Subsubsection 3.4.5.4:
L=1
Subsubsection 3.4.5.5: Spin
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Section 2.3: Other Physics
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Section 3.1: Why symmetries?
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