Liouville operator time dependency

In summary, The conversation is about someone having two questions regarding the basics of classical mechanics in their current computational physics lecture. They are unable to write formulas and had to include a picture of the equations and situation. They are asking for answers and mention using Latex in the future.
  • #1
SchroedingersLion
215
57
Hi guys,

I have a two questions concerning basics of classical mechanics.
It is to my current computational physics lecture. As I don't know how to write formulas here, I had to include the equations and the situation as a picture.

mprender.png


I would appreciate the answers.

Regards

edit: quality sucks a little bit, sorry about that ~~
 

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  • #2
SchroedingersLion said:
Hi guys,

I have a two questions concerning basics of classical mechanics.
It is to my current computational physics lecture. As I don't know how to write formulas here, I had to include the equations and the situation as a picture.

View attachment 225041

I would appreciate the answers.

Regards

edit: quality sucks a little bit, sorry about that ~~
You can use LaTeX to write formulas.
 
  • Like
Likes SchroedingersLion
  • #3
tnich said:
You can use LaTeX to write formulas.
Thanks for the hint. I will use Latex next time.
 
  • #4
*push*

=(
 

1. What is the Liouville operator?

The Liouville operator is a mathematical operator used in the study of quantum mechanics. It represents the time evolution of a quantum system by describing how the density operator of the system changes over time.

2. How does the Liouville operator account for time dependency?

The Liouville operator accounts for time dependency by including the time-dependent Hamiltonian operator in its equation. This allows for the description of the time evolution of a quantum system, taking into account any changes in the system over time.

3. What is the significance of the Liouville operator in quantum mechanics?

The Liouville operator is a fundamental component in the mathematical framework of quantum mechanics. It allows for the prediction of the behavior of a quantum system over time, providing insights into the dynamics and properties of the system.

4. How is the Liouville operator used in practical applications?

The Liouville operator is used in a variety of practical applications, such as in the study of chemical reactions, molecular dynamics, and the behavior of quantum systems in external fields. It is also used in the development of quantum algorithms and in the simulation of quantum systems.

5. What are some limitations of the Liouville operator?

One limitation of the Liouville operator is that it assumes a closed and isolated quantum system, which may not always be the case in practical applications. Additionally, it does not take into account the effects of quantum measurement and collapses, which can significantly impact the behavior of a system over time.

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