# 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 meaning of a representation in one-dimensional quantum mechanics

In many places, one reads about chosing a representation for studying a particular one-dimensional quantum system. Usual representations are the position representation, the momentum representation or ...
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### Negative kinetic energy on a step potential

I'm doing an introductory course on quantum mechanics. I'm having trouble with the explanation of the kinetic energy on the classically forbbiden region on a step potential ($V=0$ for $x<0$, $V=V_0$...
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### On which bundle do QFT fields live?

In QFT, there is a vector field of electromagnetism, usually notated by $A$, which transforms as a 1-form under coordinate changes. Since quantum fields are operator-valued, I thought it is a section ...
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### Can the Parity Operator in polar coordinates be defined as $\hat\Pi\psi(r,\theta,\phi) = \psi(r,\theta+\pi,\phi).$?

I was reading about Symmetries & Conservation Laws from Introduction to Quantum Mechanics, David J. Griffiths when I came across this question about the parity operator in three dimensions: ...
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Consider the following Lindbladian $$L \left[X \right] = i \left[H, X \right] + \gamma \left( 2QXQ - \left(Q^2X + XQ^2 \right) \right),$$ where X is observable, in other words, Heisenberg picture. ...
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### Derivation of two-body Coulomb interaction in momentum space

$\newcommand{\vec}{\mathbf}$ In Condensed Matter Field Theory by Altland and Simons, they claim the two-body Coulomb interaction for the nearly-free electron model for a $d$-dimensional cube with side ...
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### Can I use any linearly independent, orthogonal, eigenkets as starting basis to construct $S_x$, $S_y$ and $S_z$? [closed]

I know how to construct $S_z$ using $|\uparrow\rangle$=$\left(\begin{matrix}1\\0\end{matrix}\right)$ and $|\downarrow\rangle$=$\left(\begin{matrix}0\\1\end{matrix}\right)$ as starting basis. And I can ...
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### Completeness meaning (complete basis vs complete metric space) [migrated]

Today my professor started talking about the formalism of QM. We talked about that that eigenvectors of a Hermitian operator (over Hilbert space) is a "complete set". He also mentioned ...
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### I need to find the state of the system at a general time, knowing the Hamiltonian and the state at $t=0$ [closed]

The Hamiltonian for a certain three-level system is represented by the matrix $$H = \begin{pmatrix}a & 0 & b \\ 0 & c & 0 \\ b & 0 & a\end{pmatrix},$$ where $a$, $b$, and $c$ ...
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