Chapter 11. Applied Functional Analysis

  1. Prof. Dr. Charlie Harper

Published Online: 28 JAN 2005

DOI: 10.1002/3527603077.ch11

Analytic Methods in Physics

Analytic Methods in Physics

How to Cite

Harper, C. (1999) Applied Functional Analysis, in Analytic Methods in Physics, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527603077.ch11

Author Information

  1. California State University, Hayward, USA

Publication History

  1. Published Online: 28 JAN 2005
  2. Published Print: 12 OCT 1999

ISBN Information

Print ISBN: 9783527402168

Online ISBN: 9783527603077

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Keywords:

  • functional analysis;
  • stationary values;
  • Lagrange's multipliers;
  • Hamilton's variational principle;
  • Hamiltonian mechanics;
  • continuous media;
  • quantum mechanics;
  • Heisenberg picture;
  • Schrödinger picture;
  • Feynman path integral

Summary

This chapter contains sections titled:

  • Introduction

  • Stationary Values of Certain Functions and Functionals

    • Maxima and Minima of Functions

    • Method of Lagrange's Multipliers

    • Maxima and Minima of a Certain Definite Integral

  • Hamilton's Variational Principle in Mechanics

    • Introduction

    • Generalized Coordinates

    • Lagrange's Equations

    • Format for Solving Problems by Use of Lagrange's Equations

  • Formulation of Hamiltonian Mechanics

    • Derivation of Hamilton's Canonical Equations

    • Format for Solving Problems by Use of Hamilton's Equations

    • Poisson's Brackets

  • Continuous Media and Fields

  • Transitions to Quantum Mechanics

    • Introduction

    • The Heisenberg Picture

    • The Schrödinger Picture

    • The Feynman Path Integral

  • Problems