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Results tagged with hamiltonian-formalism
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user 47309
The Hamiltonian formalism is a formalism in Classical Mechanics. Besides Lagrangian Mechanics, it is an effective way of reformulating classical mechanics in a simple way. Very useful in Quantum Mechanics, specifically the Heisenberg and Schrodinger formulations. Unlike Lagrangian Mechanics, this formalism relies on a "Hamiltonian" instead of a Lagrangian, which differs from the Lagrangian through a Legendre transformation.
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Solving a simple classical Hamiltonian problem
Suppose you've been given this Hamiltonian: $H = m\ddot{x}$ and are asked to find the equations of motion. (This is a simplified version of a question given here on page 3.)
This isn't a homework pro …
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$p\ \text dq$ is the "tautological" one-form?
Here's how it finally clicked for me. Let $\phi: M \rightarrow N$ be a smooth map, and $\alpha$ be a 1-form on $N$. Recall that the pullback of $\alpha$ by $\phi$ is a 1-form $\phi^*\alpha$ on $M$ def …
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