# Tagged Questions

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 ...

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### What are the necessary/sufficient conditions for a system to be Hamiltonian/non-Hamiltonian?

I searched for a definition of Hamiltonian system on Huang and Tuckerman text but have not found anything precise. So intuitively I suppose: Hamiltonian system= a system which admits a complete ...
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### Prerequisites for classical mechanics by Susskind

So I am an undergraduate in Electrical Engineering. We had a course on Physics in our freshman year which is equivalent to Classical Mechanics I as taught in MIT. I am interested in studying advanced ...
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### Quantum phase space

Classical phase space is defined as a space in which all possible states are represented. Every state corresponds to a unique point in the phase space. On the other hand, in quantum mechanics every ...
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### Canonical transformation from Hamiltonian without external source to Hamiltonian with external source

Let a system with time-independent Hamiltonian, $H_0(q,p)$ be subjected to an external oscillating field $E_0\sin(wt)$, so that the Hamiltonian becomes $H=H_0(q,p)-qE_0\sin(wt)$. Find a canonical ...
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### Spherical phase space dynamics

I have a hamiltonian of the form $$H(\phi,z) = (1-z^2)\cos(2\phi) + \chi z^2$$ with position $\phi$ and conjugate momentum $z$. It has this form provided that $z \in [-1,1]$ and we have natural ...
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### If $(q,p)$ to $(Q,P)$ is a canonical transformation, then does this imply $(Q,P)$ to $(q,p)$ is also?

If $(q,p)$ to $(Q,P)$ is a canonical transformation, then does this imply $(Q,P)$ to $(q,p)$ is also, assuming Hamilton's equations hold for the coordinates $(q,p)$? This seems like it should be true ...
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### Ostrogradski’s theorem's proof

I am looking for a proof of the next theorem: "If the higher order time derivative Lagrangian is non-degenerate, there is at least one linear instability in the Hamiltonian of this system." Where ...
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### Determining the geometry of the phase space of a system [closed]

How do we check the geometry of the phase space ? I mean in classical mechanics we use position and conjugate momenta as a space of all possible states of the particle. How do we know that this phase ...
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### In a rigid rotor, are there “elegant” orientation coordinates that are conjugate to angular momenta?

I just was looking at the big bag-of-math wikipedia article on rigid rotors, and the section on the Hamiltonian form bugs me a bit since they are using Euler angles to represent the orientation. As a ...
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### How to find canonical transformation for given $P_i$ which are constants

We have a 2-D harmonic oscillator with Hamiltonian $H(r,\theta,p_r,p_\theta)=\frac{p_r^2}{2m}+\frac{p_\theta^2}{2mr^2}+\frac{1}{2}kr^2$. I need a canonical transformation to $(Q_1,Q_2,P_1,P_2)$ with \$...
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### Quantization conditions/ Real Scalar field

It is often written in books, the quantization conditions for classical field theory leading to Lagrangian of a real scalar field and thus to Klein Gordon equation. And these are introduced by ...