Properties of the Spectrum

Related lectures (32)

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Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

Explores the theory of bounded operators on Hilbert space, including adjoint properties and self-adjointness.

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.

Covers the duality principle in linear algebra and its implications in mathematics.

Explains the postulates of quantum mechanics and the representation of observables by operators.

Introduces linear and bounded operators, compact operators, and the Banach space.

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

Covers the proof of unitary group uniqueness and spectral types.