Linear Operators: Quantum Mechanics and Linear Algebra

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

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

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

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

Discusses measurement in Quantum Mechanics, focusing on state vectors, observables, eigenvalues, and probabilities.

Covers the basics of quantum mechanics, focusing on Hamiltonian operator and Schrödinger equations.

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