I've done basic or introductory mechanics at the level of Resnick and Halliday. I'm currently studying calculus of variations and the Lagrangian formulation of mechanics on my own. I read somewhere that an understanding of classical mechanics is necessary for appreciating quantum mechanics. Can someone please give me the big picture, where I can see the connections between classical and quantum mechanics? (I am fairly new to quantum mechanics).
Is it the case that the Lagrangian and Hamiltonian formulations are what one uses, primarily, in quantum mechanics?
Best Answer
It's been awhile since I've studied QM, but I recall it often being stated that classical mechanics was the limit of quantum mechanics as $\hbar \to 0$. Yes, the Hamiltonian approach to mechanics is often used in both. The Poisson bracket of classical Hamiltonian mechanics has it's quantum mechanical analog in the quantum mechanical commutator. IIRC, this is one way to quantize classical theories. For classical or quantum field theory, one typically works in the Lagrangian framework, where one tries to minimize some action.