Quantum Wigner master equation

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SUMMARY

The discussion centers on the Quantum Wigner master equation, specifically the equation's representation in coordinates as outlined in a referenced book. The equation is given as $$\frac{\partial\rho}{\partial t}=\frac{1}{i \hbar}[H_0,\rho]+\frac{\gamma}{i \hbar}[q,\{p,\rho\}]-\frac{D}{\hbar^2}[q,[q,\rho]]$$. The user seeks clarification on the derivation of terms in the form (x-y) within the equation. The reference provided is a book discussing quantum harmonic oscillator dissipation by Feynman.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Wigner function and its applications
  • Knowledge of Hamiltonian mechanics
  • Proficiency in mathematical notation used in quantum equations
NEXT STEPS
  • Study the derivation of the Wigner function from the density matrix
  • Learn about the implications of the Quantum Wigner master equation in quantum optics
  • Explore the concept of dissipation in quantum systems
  • Review the mathematical techniques for handling commutators in quantum mechanics
USEFUL FOR

Quantum physicists, researchers in quantum mechanics, and students studying advanced quantum theories will benefit from this discussion.

Fabio Hernandez
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I have the quantum master equation:

$$\frac{\partial\rho}{\partial t}=\frac{1}{i \hbar}[H_0,\rho]+\frac{\gamma}{i \hbar}[q,\{p,\rho\}]-\frac{D}{\hbar^2}[q,[q,\rho]]$$

And have to prove that the coordinates representation is like in the book of the link.

I can't undertand how to obtain the terms with th form (x-y), why (x-y)?.

Thanks.

Reference:
https://books.google.com.br/books?i...rmonic oscillator dissipation feynman&f=false
 
I solve it. Thanks.
 

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