From Classical to Quantum Mechanics

[Joker93]

What parts of Classical Mechanics must someone know before studying Quantum Mechanics in order to understand the former in all its glory?
Thank you

 

[bhobba]

What parts of Classical Mechanics must someone know before studying Quantum Mechanics in order to understand the former in all its glory?

For a really good understanding the Hamiltonian and Lagranian formalism. I like Landau's beautiful book that emphasises what is also very important in QM - symmetry:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Thanks
Bill

 

[Joker93]

For a really good understanding the Hamiltonian and Lagranian formalism. I like Landau's beautiful book that emphasises what is also very important in QM - symmetry:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Thanks
Bill

Is there a pathway for easily getting the idea behind the things that you mentioned?

 

[bhobba]

Is there a pathway for easily getting the idea behind the things that you mentioned?

IMHO not really.

Its not really a hard book if you know multi-variable calculus. You can do it in a week.

Thanks
Bill

 

[A. Neumaier]

What parts of Classical Mechanics must someone know before studying Quantum Mechanics in order to understand the former in all its glory?

The former or the latter?
If the former, you need some of all parts of classical mechanics, otherwise you only have part of its glory.
If the latter, does quantum field theory belong to its glory, as far as you are concerned?

 

[Joker93]

O

The former or the latter?
If the former, you need some of all parts of classical mechanics, otherwise you only have part of its glory.
If the latter, does quantum field theory belong to its glory, as far as you are concerned?

Oh no, i meant the latter!
So, the question is: What must someone know as far as Classical Mechanics are concerned in order to fully understand undergraduate Quantum Mechanics?

 

[A. Neumaier]

What must someone know as far as Classical Mechanics are concerned in order to fully understand undergraduate Quantum Mechanics?

Not very much: The Hamiltonian approach to classical dynamics, free motion, the notion of momentum and angular momentum, the 2-body problem. Also useful are the basics about classical waves and the basics of geometric optics.

Far more important is that you have a good command of linear algebra and know how to solve linear ordinary differential equations.

 

[Joker93]

Not very much: The Hamiltonian approach to classical dynamics, free motion, the notion of momentum and angular momentum, the 2-body problem. Also useful are the basics about classical waves and the basics of geometric optics.

Far more important is that you have a good command of linear algebra and know how to solve linear ordinary differential equations.

Could you tell me what kind of linear ordinary differential equations must one know before taking a first QM course? Thanks for the reply by the way

 

[A. Neumaier]

what kind of linear ordinary differential equations must one know

At least:

• single linear ODEs $\dot y(t)=a(t)y(t)+b(t)$: superposition principle, solution of the homogeneous system via integration, general solution by variation of constants.
• linear systems with constant coefficients and a driving force, $\dot y = A y + F(t)$, where $A$ is a square $n\times n$ matrix and $F(t)$ a vector valued function: exponential ansatz, superposition principle, general solution, representation of the solution in terms of the matrix exponential and a corresponding spectral decomposition of the force.

 

[sandy stone]

Speaking as an interested layman, I found that Susskind's two books (titled something like The Theoretical Minimum) give you a pretty good introduction and are not too painful. More advanced contributors may disagree.

 

[Keith_McClary]

Recent somewhat related discussion on mathoverflow, answered by Terry Tao:
Does quantum mechanics ever really quantize classical mechanics?

 

[MrRobotoToo]

Lagrangian and Hamiltonian mechanics, especially Poisson brackets and the Hamilton-Jacobi equation.

 

[mpresic]

Seems like some responder(s) forgot the Schrödinger's equation, (central to undergraduate QM) is a partial differential equation, not an ordinary differential equation. The most common technique for solving SE at the undergrad level, is separation of variables. However, this is not addressing the question, what parts of classical mechanics are necessary.
The more you understand classical mechanics the better. Many QM applications (examples will have classical analogs. To get a proper appreciation of QM you need to be prepared with CM. However, I would say at the undergrad level, if you did not do as well as you might have CM, you might still do well in QM, assuming you have a good grounding in mathematical physics. I qualify this by saying, make sure you repair any defects in CM, as soon as practical.
Caveat and silver lining: Caveat: The (first) course will not give you a complete understanding of undergraduate QM.
Silver lining: By the time you need a complete understanding of undergraduate QM, it will give you time to study the Lagrangian, and Hamiltonian Formulation of classical mechanics. Poisson Brackets, and advanced formalism can usually wait for grad school. Most students seem to find the commutator easier to understand than the classical Poisson Brackets.