Confused about symmetries and canonical transformations

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SUMMARY

The discussion centers on the concept of canonical transformations as presented in R. Shankar's "Principles of Quantum Mechanics." Participants seek clarity on the relationship between canonical transformations, symmetries, and their implications within the context of Lagrangian and Hamiltonian mechanics. The importance of understanding classical mechanics is emphasized for a solid foundation in quantum mechanics, particularly for those self-studying these principles. The forum highlights the need for a comprehensive grasp of analytical mechanics to facilitate further studies in quantum theory.

PREREQUISITES
  • Familiarity with Lagrangian mechanics
  • Understanding of Hamiltonian mechanics
  • Basic knowledge of symmetries in physics
  • Exposure to canonical transformations
NEXT STEPS
  • Study the concept of canonical transformations in detail
  • Explore the implications of symmetries in Lagrangian and Hamiltonian formulations
  • Review analytical mechanics to strengthen foundational knowledge
  • Investigate the relationship between classical mechanics and quantum mechanics
USEFUL FOR

Students and educators in physics, particularly those focusing on classical mechanics and its applications in quantum mechanics, will benefit from this discussion.

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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