Linear Operators

Quantum Mechanics · Part 1

209 KB10 sections4 key equationsLaTeX typeset
Download PDFRead Online (Free)

Table of Contents

  1. 1.2.1 Definition of Linear Operators
  2. 2.2.2 Adjoint Operator
  3. 3.2.3 Hermitian Operators
  4. 4.2.4 Unitary Operators
  5. 5.Definition
  6. 6.Matrix Representation
  7. 7.Properties of the Adjoint
  8. 8.Matrix Representation of Adjoint
  9. 9.Key Property: Real Eigenvalues
  10. 10.Examples of Hermitian Operators

Key Equations

$$\hat{A}(\alpha|\psi\rangle + \beta|\phi\rangle) = \alpha\hat{A}|\psi\rangle + \beta\hat{A}|\phi\rangle$$
$$\langle \psi | \hat{A}^\dagger | \phi \rangle = \langle \phi | \hat{A} | \psi \rangle^*$$
$$\hat{A}^\dagger = \hat{A}$$
$$\langle a | \hat{A} | a \rangle = \langle a | \hat{A} | a \rangle^*$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Mechanics course on CoursesHub.World. Master quantum mechanics from mathematical foundations to advanced topics. Covers Hilbert spaces, wave functions, angular momentum, perturbation theory, scattering, and path integrals with 450+ pages ...

← Hilbert Spaces
Representations →