Eigenvalue problem: Eigenbasis, Spectral theorem

Related lectures (32)

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

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

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

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Explores the matrix representation of operators and basis transformation in linear algebra.

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

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

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