All Questions
7 questions
0
votes
1
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55
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Which is the differential $\text{d} p_i$ of a generalized momentum?
I want to get a partition function, but I introduce a generalized momentum, my doubt is about, when I define a differential respect to $p$, it means $\text{d} p$, which is the correct form to get it?
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- 13
2
votes
1
answer
244
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Is Goldstein's matrix formalism to Hamiltonian mechanics necessary? [closed]
I am trying to see whether the matrix formalism of the Hamiltonian formalism (used in Goldstein's textbook) is truly necessary to solve problem in this framework.
It appears so based on the problem I'...
- 1,081
2
votes
1
answer
852
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Hamiltonian time-independent, partial derivative always zero?
For conceptual simplicity, let's restrict the discussion to systems with a two-dimensional phase space $\mathcal P$ with generalized coordinates $(q,p)$.
Hamiltonian is a function that maps a pair ...
- 51
4
votes
1
answer
389
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Liouville's Theorem. True or False?
In my quantum theory course, there is a question ask for checking whether the expectations in quantum and classical Liouville theory are identical.
Here is the original version:
"Assume the system ...
- 431
1
vote
3
answers
2k
views
Time derivative of a function in Phase Space
Consider a function $\mathcal{H}(q_i,p_i;t)$ such that it obeys the equation:
$$ \frac{d\mathcal{H}}{dt}=\frac{\partial\mathcal{H}}{\partial t}$$
What does this equation imply (read: mean), physically?...
- 165
2
votes
1
answer
3k
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Full time-derivative, Poisson brackets and Hamilton's equations (classical mechanics)
While studying Poisson brackets in classical mechanics and the derivation of $\dot{q_j}=\{q_j,H\}$ and $\dot{p_j}=\{p_j,H\}$ form of Hamilton's equations I encountered a surpsing identity, which led ...
- 390
5
votes
2
answers
10k
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When does the total time derivative of the Hamiltonian equal its partial time derivative?
When does the total time derivative of the Hamiltonian equal the partial time derivative of the Hamiltonian? In symbols, when does $\frac{dH}{dt} = \frac{\partial H}{\partial t}$ hold?
In Thornton &...
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