Methods of Modern Mathematical Physics Volume I Functional Analysis 1st Edition by Michael Reed, Barry Simon ISBN 0080570488 9780080570488

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ISBN 10: 0080570488 
ISBN 13: 9780080570488
Author: Michael Reed, Barry Simon

Methods of Modern Mathematical Physics, Volume I: Functional Analysis (1st Edition) by Michael Reed and Barry Simon is a foundational textbook that is highly regarded in the field of mathematical physics. It serves as the first volume in a comprehensive series that covers a variety of mathematical tools and techniques necessary for the rigorous study of physics, particularly in the realm of quantum mechanics and related fields.

Methods of Modern Mathematical Physics Volume I Functional Analysis 1st Table of contents:

• Hilbert Spaces

  • Definitions and properties of Hilbert spaces

  • Inner product spaces and orthogonality

  • Examples of Hilbert spaces used in physics

• Operators on Hilbert Spaces

  • Bounded linear operators and their properties

  • Unbounded operators and their domains

  • Examples of important operators in quantum mechanics (e.g., momentum and Hamiltonian operators)

• Spectral Theory

  • Spectral representation of operators

  • Eigenvalues and eigenvectors

  • The spectral theorem for self-adjoint operators

  • The role of spectral theory in quantum mechanics

• Self-Adjoint Operators

  • Definition and properties of self-adjoint operators

  • Spectral properties of self-adjoint operators

  • Applications to quantum mechanical observables

• Compact Operators

  • The concept of compact operators and their spectral theory

  • Properties and examples of compact operators

  • Role of compact operators in scattering theory and perturbation theory

• Applications to Quantum Mechanics

  • Mathematical formulation of quantum mechanics using functional analysis

  • The Schrödinger equation and its operator formulation

  • The role of Hilbert spaces and operators in quantum mechanics

  • Wavefunctions, observables, and the spectral theorem in physics

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