Unitary representation

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Stone-von Neumann Theorem

Explores the Stone-von Neumann Theorem and unitary operators on Hilbert spaces.

Spectral Analysis: Hyperbolic Surfaces

Explores the spectral analysis of hyperbolic surfaces through the trace formula and its applications in understanding geometric and spectral properties.

Unitary Representations: Schur's Lemma

Explains Schur's Lemma on unitary representations and their irreducibility and invariance properties.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Shor's factoring algorithm: Quantum Phase Estimation

Covers Shor's factoring algorithm and the link between order finding and factoring.

Linear Algebra: Quantum Mechanics

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

Quantum Physics I

Explores quantum state evolution, unitary operators, Heisenberg representation, spin precession, and observable averages.

Linear Algebra: Quantum Mechanics

Covers the application of linear algebra concepts to Quantum Mechanics, including spectral theorem and Brillouin zone.

Quantum Physics I

Introduces quantum physics postulates, measurement principles, and operator transformations between bases.

Deutsch Josza algorithm

Covers the Deutsch-Josza algorithm, a quantum algorithm solving problems with a single query to an oracle.