Sturm-Liouville Problem: Homogeneous Boundary Conditions Essential Role

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Linear Operators: Basis Transformation and Eigenvalues

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

Quantum Mechanics: Postulates and Observables

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

Postulates of Quantum Mechanics

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

Eigenvalue problem: Eigenbasis, Spectral theorem

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

Hermitian Operators and Spectral Theorem

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

Linear Operators: Quantum Mechanics and Linear Algebra

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

Quantum Eigenfunctions

Covers quantum eigenfunctions and the importance of A and B commuting for the same set of eigenfunctions.

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Linear Algebra: Quantum Mechanics

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

Quantum Mechanics Basics

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