# Questions tagged [hamiltonian-formalism]

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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### Can I use Hamilton-Jacobi equation here?

Suppose the Hamiltonian does not have a second impulse in it: $$H = \frac{1}{2}(q_1^2+p_1^2)F(q_2, t).$$ Can I use Hamilton-Jacobi equation here or not? I used it as is and got the same answer, as if ...
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### Solution of the classical 2D quartic oscillator

Consider a classical oscillator in two spatial dimensions with Hamiltonian $$H=\frac{1}{2}\vec{p}^2 + \frac{1}{2}\omega r^2 + ar^4.$$ This system has two conserved quantities, the energy and angular ...
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### How to do classical perturbation theory with Poisson brackets

I need some help computing the behavior of variables $c_i$ in a classical system with Hamiltonian $H$ using perturbation theory. There are as many $c_i$ variables as there are degrees of freedom. I'd ...
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### Hamilton's characteristic function, wave-particle duality and constant-action surfaces

So, I'm currently doing some research about the way in which classical physics connects to quantum physics, and I came across the Hamilton-Jacobi equation, and the implications of Hamilton's ...
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### Quantum mechanics with a classical Chern-Simons term

In this post, quantum mechanics falls under what is traditionally called "first quantization". This is in contrast to quantum field theory which traditionally falls under "second ...
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### Can we reduce the entropy of a system arbitrarily by sending out a photon after arbitrary delay?

I am not asking whether this is practically feasible given current technology. Rather I'm asking whether it is possible in principle given current laws of physics. Suppose we have a system with a ...
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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 EoM for corresponding coords? [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 ...
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### Exact solution of non-integrable Hamiltonian system?

Following this note (Introduction to Integrability – FS 2013, Lecturers: Dr. Marius de Leeuw, Dr. Constantin Candu), a system is said to be solved by quadratures if the solution can be constructed by •...
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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 ...
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### Deriving Lagrangian mechanics from Hamiltonian mechanics [duplicate]

I have just finished reading Susskind's Theoretical Minimum. I think I got it well, even found some mistakes in few equations🙈 The book starts from Newtonian Mechanics, then derives Lagrangian ...
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### Lie algebra of Hamiltonian functions

Could anyone explain to me how to obtain the Corollaries 2 and 3 in the following paragraph taken by Arnold's book? The Lie algebra of hamiltonian functions The hamiltonian vector fields on a ...
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I'm studying a complex scalar field theory in a spatially flat FLRW background. Using the standard conformal time metric $$ds^2 = dt^2 - a^2(dr^2 - r^2 d\Omega_2^2)$$ (where $a$ is the scale factor), ...