Book on Classical and Quantum Mechanics

[Reedeegi]

Is there a book that presents classical and quantum mechanics utilizing the same mathematical framework? Just to get it out of the way, I have books on both topics that are separate from each other, I'm merely interested in any formulations of both theories utilizing the same math frameworks. If possible, is there also a book that describes classical and quantum geometry?

 

[dx]

Check out Robert Geroch's lecture notes called "Geometric Quantum Mechanics".

 

[charng]

Yes, there are several books that present classical and quantum mechanics using the same mathematical framework. One example is "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine, which presents both classical and quantum mechanics using the mathematical framework of Hilbert spaces and operators. Another example is "Classical and Quantum Mechanics: The Hamiltonian Approach" by Walter Greiner, which also uses the same mathematical framework for both theories.

In terms of classical and quantum geometry, there are also books that discuss the relationship between the two. One example is "Geometry of Quantum Mechanics: An Introduction to Quantum Theory" by Ingemar Bengtsson and Karol Zyczkowski, which explores the connection between classical and quantum geometries. Another example is "Quantum Geometry: A Framework for Quantum General Relativity" by Giampiero Esposito, which discusses the use of geometry in both classical and quantum theories of gravity.

It is important to note that while classical and quantum mechanics share some mathematical similarities, they also have fundamental differences that cannot be fully reconciled. Therefore, any book claiming to present both theories using the same mathematical framework should be approached with caution and critically evaluated.