What concepts/math from junior-level CM for a QM class?

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In summary, a physics major in junior year who missed out on a classical mechanics class is preparing for a quantum mechanics class next semester. They are advised to review the Hamiltonian and Hamiltonian equations of motion, angular momentum, and other concepts. They are recommended to use Susskind's lectures and a book by Marion and Thornton for studying classical mechanics. It is mentioned that a detailed knowledge of classical mechanics is not necessary for understanding quantum mechanics.
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Intrinsic3141
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Hey everyone, I'm a physics major in junior year that missed out on my classical mechanics class this fall semester because of some prereq stuff. I emailed the professor teaching QM next semester and got in without the necessary classical prereq. He said I should go over "the Hamiltonian and Hamiltonian equations of motion, angular momentum, and some others."

I plan on going over this stuff this winter break, and was wondering what other concepts I might need and where/how to study and review them. Any good books/resources? Thanks.
 
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  • #2
I think Susskind's lectures on classical mechanics could be a good resource he introduces the CM necessary for QM but its not enough:
http://www.subplanck.com/self-study...e-by-dr-leonard-susskind-stanford-university/
Classical Dynamics of Particles and Systems (Marion and Thornton) is a good book on the subject
also there are these lectures on classical mechanics by Balakrishnan:
http://www.youtube.com/watch?v=Q6Gw08pwhws&feature=channel

I don't think you need a detailed knowledge of CM to understand QM.
 
  • #3
Judging from most junior level QM classes I've heard about, you'll be just fine. Even if you don't know what a hamiltonian is, it will probably be explained. The knowledge of classical mechanics certainly can enrich the quantum mechanics, but usually isn't essential the first time through where you focus primarily on the physics rather than the mathematical formalism (sometimes relegated even to a side note!).
 

1. What are the key concepts in classical mechanics that are important for understanding quantum mechanics?

The key concepts in classical mechanics that are important for understanding quantum mechanics include Newton's laws of motion, conservation of energy and momentum, and the principle of least action. These concepts provide the foundation for understanding the behavior of particles in classical systems, which can then be extended to quantum systems.

2. What mathematical tools are commonly used in junior-level classical mechanics courses that are also relevant for quantum mechanics?

Some of the common mathematical tools used in junior-level classical mechanics courses that are also relevant for quantum mechanics include calculus, linear algebra, and differential equations. These mathematical tools are used to describe the behavior of particles and systems in both classical and quantum mechanics.

3. How does uncertainty in classical mechanics differ from uncertainty in quantum mechanics?

In classical mechanics, uncertainty is typically associated with a lack of knowledge about the initial conditions of a system. In quantum mechanics, uncertainty is an inherent property of the system itself, as described by Heisenberg's uncertainty principle. This means that even with perfect knowledge of the initial conditions, there will always be some degree of uncertainty in the measurements of certain observables.

4. How do symmetries play a role in both classical and quantum mechanics?

Symmetries play a crucial role in both classical and quantum mechanics. In classical mechanics, symmetries are used to describe the behavior of particles and systems, such as conservation laws for energy and momentum. In quantum mechanics, symmetries are used to classify and understand the properties of particles and their interactions, as well as to predict the behavior of systems.

5. Are there any limitations to using classical mechanics concepts and math in quantum mechanics?

While classical mechanics concepts and math can provide a good foundation for understanding quantum mechanics, there are limitations to their applicability. In quantum mechanics, particles often behave in ways that are counterintuitive and cannot be described by classical concepts, such as superposition and entanglement. Additionally, the mathematical tools used in classical mechanics may not be sufficient to fully describe the behavior of quantum systems.

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