Concept
Unitary representation
Related lectures (36)
Spherical Hecke Algebra: Irreps and Eigenspaces
Covers the spherical Hecke algebra and finite-dimensional unitary representations.
Eisenstein Series: Decomposition and Unitarizability
Covers the decomposition of Eisenstein series into orthogonal components and the unitarizability of certain representations.
Unitary Operators: Translation and Transformation
Explores unitary operators for translation and transformation in quantum mechanics.
Scattering Amplitude and Optical Theorem
Covers the introduction of scattering amplitude, optical theorem, and unitary operators in quantum mechanics.
Unitary Representations: Schur's Lemma
Explains Schur's Lemma on unitary representations and their irreducibility and invariance properties.
Shor's factoring algorithm: Quantum Phase Estimation
Covers Shor's factoring algorithm and the link between order finding and factoring.
Extension of Linear Transformations
Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.
Quantum Physics I
Explores quantum state evolution, unitary operators, Heisenberg representation, spin precession, and observable averages.
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.