Density Matrix
Quantum Mechanics · Part 9
224 KB10 sections4 key equationsLaTeX typeset
Table of Contents
- 1.Definition and Motivation
- 2.Properties of Density Matrices
- 3.Expectation Values and Measurements
- 4.Time Evolution
- 5.Reduced Density Matrix and Partial Trace
- 6.Purity and Mixedness
- 7.Von Neumann Entropy
- 8.Bloch Sphere Representation (Qubits)
- 9.Quantum Operations and CPTP Maps
- 10.Applications
Key Equations
$$\hat{\rho} = |\psi\rangle\langle\psi|$$
$$\langle A \rangle = \text{Tr}(|\psi\rangle\langle\psi|\hat{A}) = \langle\psi|\hat{A}|\psi\rangle$$
$$\hat{\rho}_A = \text{Tr}_B(\hat{\rho}_{AB}) = \sum_i \langle b_i|\hat{\rho}_{AB}|b_i\rangle$$
$$S(\hat{\rho}) = -\text{Tr}(\hat{\rho}\ln\hat{\rho}) = -\sum_i \lambda_i \ln\lambda_i$$
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 ...
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