# Questions tagged [canonical-conjugation]

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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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### Commutation relation between charge number and phase in superconductors

Consider an isolated Cooper pair box. The charge number operator is $$\hat{n} = \sum_{n=-\infty}^{+\infty} n |n\rangle \langle n|$$ where $|n \rangle$ is the state in which $n$ Cooper pairs have ...
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### Relation between energy and time

I would like help in understanding something that has been causing me a lot of trouble recently: Why is energy always related to time in physics? Examples include the 4-momentum, the energy-time ...
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### Conjugate observables - can the commutation relations be generalised?

Conjugate variables are variables that are Fourier transforms of one another (that is they are Fourier transform duals) and consequently have an uncertainty relation existing between them. In quantum ...
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### Why does the Pauli objection not disqualify the existence of the position operator?

According to the Pauli objection (see for example here or the answer to this question) there can be no time operator $\hat{T}$ canonically conjugate to the Hamiltonian $\hat{H}$ of a physical system ...
1 vote
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### Canonical transformations in Quantum Mechanics

Heisenberg's famous commutator of a pair of conjugated canonical variables is formulated for position and conjugated momentum $$[q,p] = i\hbar.$$ Intuitively I would guess that it would also work ...
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### Lagrangian and Hamiltonian Mechanics: Conjugate Momentum

I am a physics undergraduate student currently taking a classical mechanics course, and I am not able to understand what conjugate/canonical momentum is (physically). It is sometimes equal to the ...
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