Weeks | Topics |
1 |
Definitions of Matricies, Eigenvalues and Eigenvectors, The Concept of a Vector Space, Inner Product Spaces
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2 |
Hilbert Spaces, Linear Operators, Bilinear Forms, Linear Functionals, Direct Product Spaces
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3 |
The Concept of a Group, Group of Rotations, Group of Translations
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4 |
The Group of the Schrödinger Equation, The Role of Matrix Representations
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5 |
Some Elementary Considerations, Classes, Invariant Subgroups, Cosets, Factor Groups, Homomorphic and Isomorphic Mappings, Direct Products and Semi-direct Products of Groups
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6 |
Definitions on Representations of Groups, Equivalent Representations, Unitary Representations, Reducible and Irreducible Representations, Schur’s Lemmas
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7 |
Projection Operators, Direct Product Representations, The Wigner-Eckart Theorem, Representations of Direct Product Groups, Irreducible Representations of Finite Abelian Groups, Induced Representations
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8 |
Midterm
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9 |
The Solution of the Schrödinger Equation, Transition Probabilities and Selection Rules, Time-independent Perturbation Theory
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10 |
The Bravais Lattices, The Cyclic Boundary Conditions, Irreducible Representations of the Group T of Pure Primitive Translations, Bloch’s Theorem
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11 |
Brillouin Zones, Electronic Energy Bands, Survey of the Crystallographic Space Groups
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12 |
Fundamental Theorem on Irreducible Representations of Symmorphic Space Groups, Irreducible Representations of the Cubic Space Groups Oh1, Oh5 and Oh9
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13 |
Degeneracies of Eigenvalues and the Symmetry of E(k), Continuity and Compatibility of the Irreducible Representations of G0(k)
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14 |
Origin and Orientation Dependence of the Symmetry Labelling of Electronic States, Character Tables for the Crystallographic Point Groups
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