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There are different ways of describing quantum mechanics. Each has its individual strength and weaknesses, but in terms of observable predictions, they are all equivalent.
Traditional Roadmap
newtonian_mechanics | Newton's laws | |||||||||||||
Lagrangian Formalism | Euler-Lagrange equation, Noether's theorem, configuration space | |||||||||||||
Hamiltonian Formalism | Hamilton's equation, canonical transformation, generating functions, Noether's theorem in the Hamiltonian formalism, phase space | |||||||||||||