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# Questions tagged [poisson-brackets]

In phase-space classical Hamiltonian mechanics, the Poisson bracket is an antisymmetric binary operation acting like a derivative.

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### How can you confirm that two variables are canonically conjugate using Poisson brackets?

Suppose you have two conjugate variables $q$ and $p$ that are canonically transformed into two other variables $Q$ and $P$. What needs to hold true for these variables in terms of Poisson brackets? I ...
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### verify canonically conjugate variables by way of Poisson brackets

How do I verify using Poisson brackets that a set of variables are canonically conjugate? It's for a homework problem but I'm interested in a general approach/reference if possible. We are using ...
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### Qualitatively connecting classical Poisson brackets and quantum commutators

I have read many answers on the correspondence between classical Poisson brackets and quantum commutators, but I was wondering if it was able to be spelled out in simple words. In this answer (What is ...
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### Analogous structure of Diffusion and Schrödinger equation and definition of flux?

I came across some analogous structure of diffusion and the quantum mechanical particle (Schrödinger eq.). I have seen that there have been similar questions asked, but the (probablitily flux and the ...
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### Validity of Canonical Quantization

I was studying about what does it mean canonical quantization treatment. But now I have the next question. Why if we establish canonical the commutation relations \left[q,p\right]=i\hbar,\quad \left[...
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I am aware of two definitions of canonical transformations which I state below. Definition $1$ We go from old set of $\{q_i,p_i,t\}$ of $2n$ phase space variables to a new set \$\{Q(q_i,p_i,t),P(q_i,...