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I want to self-study QM, and I've heard from most people that Hamiltonian mechanics is a prereq. So I wikipedia'd it and the entry only confused me more. I don't know any differential equations yet, so maybe that's why.

  • But what's the difference between Hamiltonian (& Lagrangian mechanics) and Newtonian mechanics?

  • And why is Hamiltonian mechanics used for QM instead of Newtonian?

  • Also, what would the prereqs for studying Hamiltonian mechanics be?

Qmechanic
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user14445
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2 Answers2

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I'd say there were almost no prerequisites for learning Langrangian and Hamiltonian mechanics.

First thing to say is that there's almost no difference between them. They're both part of the same overarching framework. Basically it's a convenient way to write down general laws of physics. There's nothing too difficult or scary about it, and it's a lot more elegant than Newtonian theory.

If you have a rough grasp of basic physics, I don't think you need to formally learn Newtonian theory first. I had to as an undergraduate and it was a horrible mess. I've never needed to do anything using purely Newtonian theory since.

You might need to know how to solve differential equations, both ordinary and partial, but it's possible to pick this up as you go along. There's almost no linear algebra needed, so don't worry about that.

If you're looking for a book, the best one is Landau and Lifschitz, Volume I. Their exposition is very clear and concise, ideal in a textbook! Good luck!

Edward Hughes
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In university, here is the way the material was presented to me:

  1. Newtonian Mechanics
  2. Learn solutions to ODE and PDE
  3. Lagrangian Mechanics
  4. Hamiltonian Mechanics

This was over two course, back to back. Hamiltonian and Lagrangian Mechanics provide a formalism for looking at problems using a generalized coordinate system with generalized momenta. Hamiltonians and Lagrangians are written in terms of energy, a departure somewhat from Newtonian mechanics, if I recall properly.

Hamiltonian Mechanics is suitable for quantum mechanics in that one can describe a system's energy in terms of generalized position and momentum. Newtonian mechanics is for macro scale systems, like throwing a baseball. Quantum mechanics is on a much smaller scale. It is the only way I have been taught QM and it is the only way in which I've seen it taught.

Prerequisites for Hamiltonian mechanics would be solving ODEs and PDEs, familiarity with matrix operations and some linear algebra. This would do well for Hamiltonian mechanics through beginners Quantum Mechanics. Books for starting; I would recommend Boas (Mathematical Methods of the Physical Sciences) and Arfkan (Mathematical Methods for Physicists, Sixth Edition; another math methods book). For classical mechanics, Taylor Classical Mechanics. For intro QM, Giffiths Introduction to Quantum Mechanics (2nd Edition).

Best of luck!

Josh Pinto
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Dylan O. Sabulsky
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