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Where would you say I can start learning about Hamiltonians, Lagrangians ... Jacobians? and the like?

I was trying to read Ibach and Luth - Solid State Physics, and suddenly

(suddenly a Hamiltonian pops up. and then a wave equation and then $H_{aa}\ and\ H_{ab}$?

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Well, for solid state physics, you should know quantum mechanics first, which will teach you about Hamiltonians. So pick up any standard undergrad quantum text. Lagrangians don't come into undergrad QM too much, unless you happen to get an introduction to path integrals, so if you want to learn about those I'd suggest a classical mechanics text (again, any standard undergrad book will do).

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Can you elaborate on a suggested undergrad text? I've heard some are quite bad. –  Eiyrioü von Kauyf Sep 1 '12 at 15:39
    
@EiyrioüvonKauyf you need to look in a standard undergraduate text such as Classical Mechanics by John Taylor –  Physiks lover Sep 2 '12 at 10:33
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