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Results tagged with operators
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user 27396
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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What periodic functions of the angle operator are Hermitian?
Let $\hat{\theta}$ be one of the position operators in cylindrical coordinates $(r,\theta,z)$. …
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Does spin have anything to do with a rate of change?
The orbital angular momentum of a particle can be related to the revolution of that particle about some external axis. But in quantum mechanics, the spin angular momentum of a particle can't really b …
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Can spin be related to a shift in angle?
If $\hat{T}(\Delta x) = e^{-\frac{i}{\hbar}\hat{p}\Delta x}$ is the spatial translation operator, then there exists a function $f$ from $\mathbb{R}$ to the ket space $V$ such that $\hat{T}(\Delta x) f …
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What Lie group structure is used for infinite-dimensional Unitary Groups in Quantum Mechanics?
Given an infinite-dimensional Hilbert space $H$, the set $U(H)$ of all unitary operators on $H$ forms a group, known as the unitary group. … Now several subgroups of this group play an important role in quantum mechanics, for instance the group of time-translation operators and the group of spatial translation operators. …
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How are anyons possible?
If $|\psi\rangle$ is the state of a system of two indistinguishable particles, then we have an exchange operator $P$ which switches the states of the two particles. Since the two particles are indisti …
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Why isn't momentum a function of position in quantum mechanics?
(There is another operator called $\hat{\theta}$, which is one of the position operators in spherical coordinates, but that has nothing to do with spin and the $\theta$ that I'm talking about; it's related …
- 2,989
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Is there an Ehrenfest-like result for the expectation value of orbital angular momentum?
If not, is there any way to relate $\langle L_z\rangle$ to the time derivatives of expectation values of one or more operators? …
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