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Concept

Unbounded operator

Related lectures (32)

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

Quantum Physics II: Operator or Density Matrix

Explores operator or matrix density in quantum physics, discussing system evolution and interactions with the environment.

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

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Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

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

Domain and Graph of Unbounded Operators

Covers the fundamental concepts of unbounded operators in quantum physics, focusing on defining a functional calculus and spectral decomposition.

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

Essential Adjoints: Spectral Decomposition and Symmetric Operators

Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.

Hermitian Operators and Spectral Theorem

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

Spectral Decomposition of Unbounded Operators

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

Matrix Representation of Operators and Basis Transformation

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

Linear Operators: Quantum Mechanics and Linear Algebra

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

Eigenvalue problem: Eigenbasis, Spectral theorem

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

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Explores practical aspects of operator overloading in C++, emphasizing the importance of careful implementation to avoid performance issues.

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Explores the spectral theory of non-bounded operators and the importance of closed operators for spectral decomposition.

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