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Results tagged with hamiltonian-formalism
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user 202011
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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Preservation of exact equations of motion in time-dependent perturbation theory for the Hami...
From the Hamilton-Jacobi formalism the solution for the unperturbed hamiltonian $H_0$ has a generating function $S(q,\alpha,t)$ such that
$$K_0 = H_0(q, \frac{\partial S}{\partial q},t) + \frac{\parti …
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How does $\dot{q}_i p_i - H = \dot{Q}_i P_i - K + \frac{d}{dt}F$ will give the same EL and E... [duplicate]
How does $\dot{q}_i p_i - H = \dot{Q}_i P_i - K + \frac{d}{dt}F$ give the same Euler-Lagrange equations and Equations of motion (EoM) for corresponding coordinates and allow us to determine a canonica …
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Are Hamilton’s equations time-independent from it’s general derivation?
The general derivation of Hamilton’s equations involve the change in the Hamiltonian and consequently the change in the Lagrangian that is a function of $q$ and $\dot q$, $L(q,\dot q)$. This is shown …
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Are the canonical momentum and the corresponding generalized coordinates independent? [duplicate]
I know that for a lagranian $L=L(q_i, \dot{q_i},t)$ the canonical momentum is given by $p_i = \frac{\partial L}{\partial \dot{q_i}}$. The lagrangian being a function of the generalized coordinate, I w …
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