Sunday, 29 October 2017

Lecture 08 - Spectra and perturbation theory (Schuller's Lectures on Quantum Theory)

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Video Lecture: Summary of contents:  resolvent map and resolvent set of an operator; spectrum of an operator; eigenvalues and eigenv...
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Wednesday, 25 October 2017

Lecture 07 - Self-adjoint and essentially self-adjoint operators (Schuller's Lectures on Quantum Theory)

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Video Lecture: Summary of contents:  densely defined and adjoint operators, proof of well-definedness; adjoint of sum; kernel and ra...

Lecture 25 - Covariant Derivatives (Schuller's Geometric Anatomy of Theoretical Physics)

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Video Lecture: Summary of contents:  proof of the equivalence of local sections and G-equivariant functions; linear actions on assoc...
Thursday, 19 October 2017

Lecture 06 - Integration of measurable functions (Schuller's Lectures on Quantum Theory)

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Video Lecture: Summary of contents:  characteristic and simple functions; integration of non-negative, measurable, simple functions;...
Saturday, 14 October 2017

Lecture 05 - Measure Theory (Schuller's Lectures on Quantum Theory)

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Video Lecture: Summary of contents:  sigma-algebras; De Morgan's Laws; measurable spaces and measurable subsets; extended real l...
Friday, 6 October 2017

Lecture 24 - Curvature and Torsion on Principal Bundles (Schuller's Geometric Anatomy of Theoretical Physics)

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Video Lecture: Summary of contents:  exterior covariant derivative; curvature two-form; characterisation of the curvature two-form w...

Lecture 23 - Parallel Transport (Schuller's Geometric Anatomy of Theoretical Physics)

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Video Lecture: Summary of contents:  horizontal lifts of a curve to the principal bundle; ODE characterising horizontal lifts; expli...
Tuesday, 3 October 2017

Lecture 04 - Projectors, bras and kets (Schuller's Lectures on Quantum Theory)

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Video Lecture: Summary of contents:  projection and orthogonal complement; infinite-dimensional Pythagoras' theorem; open and cl...
Sunday, 1 October 2017

Lecture 03 - Separable Hilbert spaces (Schuller's Lectures on Quantum Theory)

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Video Lecture: Summary of contents:  Hilbert spaces; norm induced by an inner product; proof of the Cauchy-Schwarz inequality; proof...
Tuesday, 26 September 2017

Lecture 02 - Banach Spaces (Schuller's Lectures on Quantum Theory)

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Video Lecture: Summary of contents:  metric spaces; converges of sequences; Cauchy sequences; completeness; norms and normed spaces;...
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