Confused about symmetries and canonical transformations

AI Thread Summary
The discussion centers on the confusion surrounding canonical transformations in classical mechanics, as presented in R. Shankar's "Principles of Quantum Mechanics." Participants seek clarity on the concepts of Lagrangian and Hamiltonian methods, emphasizing the importance of understanding these classical mechanics principles for their studies in quantum mechanics. They express a lack of background in analytical mechanics, which complicates their comprehension of the material. The significance of symmetries and their consequences in the context of canonical transformations is also highlighted. A deeper understanding of these concepts is deemed essential for advancing in quantum mechanics.
Sillyboy
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this is a problem confusing me, which is in the book named Principles of Quantum Mechanics by R. Shankar. This problem is not about quantum mechanics, but just in the chapter of Review of Classical Mechanics. (The ******** is just to avoid to be deleted).

The problem is in the attachment, first I have to sorry about my expression in English.
Please make it clear that what is canonical transformation(I just know some kind of comprehension in the book, I want your guy's comprehension about Lagrangian and Hamiltonian mathod, the canonical transformations, the symmetries and their consequences)
I am here expecting your comprehension and reply to my problem.

I didn't study the analytical mechanics, but now we are self-studying the principles of quantum mechanics in the dicussion class! Hence, we do not have a good comprehension about the classical mechanics. But we think it is very important for our further study.
 

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Why?
Please answer me!
 
Sillyboy said:
Why?
Please answer me!

They're some transformations that allow us to use Hamiltonian formulation in the new coordinates.
http://en.wikipedia.org/wiki/Canonical_transformation#Notation

PS: You should be careful with the usage of exclamation, it looks like yelling.
 
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