- #1
Frost_Xue
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Hi, I don't understand how to use 51 get 66. Can you help me with that?
About Glauber's formula(or special Baker–Campbell–Hausdorff
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In summary, the conversation discusses a replacement in a mathematical equation involving a commutator and how the order is reversed on both sides of the equation. The individual asking for help does not understand how the t comes in, and the other person explains that the order of the commutator on the right hand side needs to be taken into account. The conversation also mentions a book titled "Quantum Mechanics" by C. Cohen-Tannoudji et al.
Hi, I don't understand how to use 51 get 66. Can you help me with that?
- #2
blue_leaf77
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Make the following replacement: ##F(B) = e^{At}## and ##A=B##.
- #3
Frost_Xue
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ok if I replace F(B) = e^At then should it be [A,B](e^At)' ? how does the t come from? and what do you mean by A=B? also the order of commutator seems reversed shouldn't it be negative then?blue_leaf77 said:
Sorry I am stupid.
- #4
blue_leaf77
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##(e^{At})' = \frac{d}{dA}e^{At}##.
Yes, the order is reversed on both sides of the equation. So there will be negative sign in each side and they can cancel out.
Yes, the order is reversed on both sides of the equation. So there will be negative sign in each side and they can cancel out.
- #5
Frost_Xue
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oh I didn't pay attention on the order of the commutator on the right hand side. Thank you so much for the help and time. And sorry for bothering you again.blue_leaf77 said:
- #6
blue_leaf77
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No worry, it's not a big deal.
- #7
annaphys
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Which book is this from?
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C. Cohen-Tannoudji et al. - Quantum Mechanics.
FAQ: About Glauber's formula(or special Baker–Campbell–Hausdorff
1. What is Glauber's formula?
Glauber's formula, also known as the special Baker–Campbell–Hausdorff formula, is a mathematical formula used in quantum mechanics to calculate the time evolution of operators in a quantum system. It is named after the German physicist Roy J. Glauber, who first derived it in the 1960s.
2. How is Glauber's formula used in quantum mechanics?
Glauber's formula is used to calculate the time evolution of operators in a quantum system. It can be used to determine the probability of a quantum system transitioning from one state to another over a certain period of time. This is important in understanding and predicting the behavior of quantum systems.
3. What is the significance of Glauber's formula in quantum mechanics?
Glauber's formula is significant in quantum mechanics because it allows for the calculation of the time evolution of operators in a quantum system without having to solve the Schrödinger equation. This can greatly simplify calculations and provide valuable insights into the behavior of quantum systems.
4. Are there any limitations to Glauber's formula?
Yes, there are limitations to Glauber's formula. It is only valid for systems with a finite number of degrees of freedom and cannot be applied to systems with an infinite number of degrees of freedom, such as field theories. Additionally, it may not be accurate for systems with strong interactions or highly excited states.
5. How does Glauber's formula relate to other mathematical formulas in quantum mechanics?
Glauber's formula is related to other mathematical formulas in quantum mechanics, such as the Baker–Campbell–Hausdorff formula and the Magnus expansion. These formulas are used to simplify calculations and provide a more accurate description of the time evolution of operators in quantum systems. Glauber's formula is a special case of the Baker–Campbell–Hausdorff formula, which is a more general formula used in Lie theory.