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Results tagged with operators
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user 206319
In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!
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How does the the Landé g-factor change?
In my statistical physics book, it is said that, when a particle with total angular momentum $\vec J$ is placed in a weak external magnetic field, it has a dipole magnetic moment equal to $$\hat {\vec …
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Eigenvalues of Exchange Operator
$\hat P$ is the exchange operator, the standard derivation of its eigenvalues, $\pm 1$, takes advantage of the fact that exchanging the particles two times changes nothing. Mathematically: $$\hat P \h …
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Quantum mechanics, angular momentum in spherical coordinates
I've seen many times the angular momentum operators $\hat L_x, \hat L_y,\hat L_z$ expressed in spherical coordinates but I've never seen the components operators $\hat L_\rho, \hat L_\theta, \hat L_\phi …
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Physical meaning of the operator under symmetry transformations
A symmetry transformation is a transformation on the states that can be seen as $$|\phi\rangle'=\hat U |\phi\rangle$$ Then imagine we have an observable $\hat A$ and a state $|\phi\rangle$ such that $ …
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Symmetry transformations: a doubt about the relations that we assume true
When we deal with symmetry transformations in quantum mechanics we assume true that,
If before the symmetry transformation we have this
$ \hat A | \phi_n \rangle = a_n|\phi_n \rangle,$
and after th …
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Operators of the special orthogonal group $\mathrm{SO}(3)$ in 3 dimensions
I'm confused because I thought that $\mathrm{SO}(3)$ was a group of matrices, can I say instead that all the operators that rotate a certain tensor form a $\mathrm{SO}(3)$ group? …
- 1,978
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Symmetry in quantum mechanics
My professor told us that in quantum mechanics a transformation is a symmetry transformation if $$ UH(\psi) = HU(\psi) $$
Can you give me an easy explanation for this definition?
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