# Questions tagged [operators]

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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### The definition of the weaker notion of symmetry in the sense of Wigner's theorem

The weaker notion of symmetry, in the sense of Wigner's theorem, is a transformation on the states that leave all quantum mechanical amplitudes invariant. This tells that such transformations are ...
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### The Eigenstates of a Symmetric Operator

Good Afternoon, By definition, an observable $O$ for a system of N identical particles is symmetric just in case $\langle\psi|O|\psi\rangle = \langle\psi|P^{\dagger}OP|\psi\rangle$ for any permutation ...
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### Are there Feynman diagrams for dimension-6 operator?

This document https://arxiv.org/abs/1008.4884 presents in Tables 2 and 3 the mathematical expression of many dimension-6 operators, for example (just an example) The mathematical expression does not ...
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### In the Schrödinger equation, is there an operator associated with $V$ as there is with $T$ (in the Hamiltonian)?

In the Schrödinger equation we can see an operator associated with the position This operator is used in the expression for the kinetic energy $T$, being part of the quantum mechanical Hamiltonian. ...
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### Invariance of differential operators

How do we prove that del operator is invariant under any kind of change of coordinates, specifically under galilean transformations? I am getting an extra term containing the relative velocity of two ...
Suppose we have a depolarizing channel operation $$E(\rho)=\frac{p}{2}\textbf{1}+(1-p)\rho$$ acting on a Spin$\frac{1}{2}$ density matrix of the form \$\rho=\frac{1}{2}(\textbf{1}+\textbf{s}\cdot\...
In the beginning quantum mechanics is introduced by representing the states as cute little complex vectors, for example: $$|a\rangle=a_+|a_+\rangle+a_-|a_-\rangle$$ this is a complex vector ...