Linked Questions
19 questions linked to/from What is the physical meaning of commutators in quantum mechanics?
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What is the physical meaning of commuting in quantum mechanics? [duplicate]
In quantum mechanics, if two observables commute, then perfect knowledge can be gained about both observables simultaneously.
But what does the commutator actually, physically represent?
Like ...
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111
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15
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Why quantum mechanics?
Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
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What is $\Delta t$ in the time-energy uncertainty principle?
In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to ...
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What is the Physical Meaning of Commutation of Two Operators?
I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (...
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The geometrical interpretation of the Poisson bracket
"Hamiltonian mechanics is geometry in phase spase."
The Poisson bracket arises naturally in Hamiltonian mechanics, and since this theory has an elegant geometric interpretation, I'm interested in ...
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Does the poisson bracket $\{f,g\}$ have any meaning if neither of $f$ or $g$ is the system's Hamiltonian?
Say one has a mechanical system with hamiltonian $H$, and two other arbitrary observables $f,g$. $H$ is super useful since $\{H, \cdot\} = \frac{d}{dt}$. But does $\{f,g\}$ give any useful information ...
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What is the physical meaning of anti-commutator in quantum mechanics?
I gained a lot of physical intuition about commutators by reading this topic.
What is the physical meaning of commutators in quantum mechanics?
I have similar questions about the anti-commutators. ...
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Reason for Uncertainty principle
$$\Delta x \Delta p_x \geq \frac{\hbar}{2} $$
I understand what does Heisenberg's uncertainty principle states i.e. it's definition and it has been proven experimentally. But, can anyone please ...
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What is the physical interpretation of the Poisson bracket [duplicate]
Apologies if this is a really basic question, but what is the physical interpretation of the Poisson bracket in classical mechanics? In particular, how should one interpret the relation between the ...
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Why do we care about the canonical commutation relations?
Suppose $\hat{x}$ and $\hat{p}$ are the position and momentum operators, it can be shown that
$$[\hat{x}, \hat{p}] = i\hbar\mathbb{I}.$$
The Stone-von Neumann theorem tells us that that the above is ...
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Constants of motion in quantum mechanics
What is the meaning of a constant of motion in quantum mechanics (an observable-operator that commutes with the Hamiltonian) in contrary with classical mechanics?
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Whence the $i$ in QM Poisson bracket definition?
On p. 87 of Dirac's Quantum Mechanics he introduces the quantum analog of the classical Poisson bracket$^1$
$$ [u,v]~=~\sum_r \left( \frac{\partial u}{\partial q_r}\frac{\partial u}{\partial p_r}- \...
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Commutator and Order of Measurement
I was going through Prof. Leonard Susskind's lectures on Quantum Field Theory (Lec 2). Professor said that the commutator of two observables $AB-BA$, has nothing to do with the 'measurement'- B ...
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Similarity between unitary operators and ladder operators
I observed a similarity. Is this a co-incidence?:
$$(I+\epsilon P)|x\rangle =|x+\epsilon\rangle$$
And,
$$(X+iP)|n\rangle=A_n|n+1\rangle$$
Here, $|x\rangle$ is an eigenfunction of position. $|n\rangle$ ...
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The Physical Meaning behind a Commutator [duplicate]
I've just been introduced to the idea of commutators and I'm aware that it's not a trivial thing if two operators $A$ and $B$ commute, i.e. if two Hermitian operators commute then the eigenvalues of ...
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