Stone's theorem on one-parameter unitary groups

Related lectures (32)

Explores the Wigner theorem, translation symmetry, eigenstates, and wave functions in quantum physics.

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

Introduces Hilbert operators, covering their properties, C*-algebras, and the Fourier transform's unitarity.

Covers the full quantum theory of atom-field interaction and the synthesis of arbitrary quantum states using unitary evolution operators.

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

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

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

Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Explains the Quantum Phase Estimation (QPE) algorithm and its complexity using two registers and SWAP gates.

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Explores Quantum Phase Estimation fundamentals, challenges, and applications in quantum computing.

Page 2 of 2