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 $\times$, $+$!
279 questions from the last 365 days
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Dyson series expression for the two-point Green function
On Chapter 7 of Fetter & Walecka, the authors prove Dyson formula for the (imaginary time) propagator $U(t,t_{0}) = e^{H_{0}t_{0}}e^{-H(t_{0}-t)}e^{-H_{0}t}$, where I am ommitting the $\hbar$'s. ...
- 251
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37
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The physical meaning of the "coupling operator"
I am reading Vassili N. Kolokoltsov's paper arXiv:2505.14605, "On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States", and having trouble understanding the ...
2
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1
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Does Wigner's theorem only imply left inverse?
From wikipedia
https://en.wikipedia.org/wiki/Wigner%27s_theorem
For unitary case
$$\langle U \Psi, U \Phi \rangle = \langle \Psi, \Phi \rangle .\tag{1} $$
If I apply the definition of adjoint
https://...
- 63
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A paradox in using completeness relation $\sum |\rangle\langle|=1$ of quantum mechanics
Suppose we compute an expectation value of $r_{12} r_{13}^{-1}$ over a wave function $\phi_p (1) \otimes \phi_q(2) \otimes \phi_r (3)$, we denote it as $$\langle pqr | r_{12} r_{13}^{-1} |pqr \rangle. ...
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4
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Physical meaning of a complete set of compatible observables
I am a Math student, new at Quantum Mechanics, and I am having some troubles understanding the physical meaning of the notion of “complete set of compatible observables". I know its mathematical ...
- 267
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1
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Question about Schrödinger equation with scalar and vector potentials from Sakurai
This is from page 127 of Sakurai QM:
How did they obtain this result? I understand the factor comes from the Hamilton on the LHS, but how were they able to pull out the factor out of the bra-ket like ...
4
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1
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132
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Is the commutator of field operators in an interacting theory always a $c$-number?
I understand that the commutator of field operators in a free field theory is always a $c$-number. Now I want to see whether a generalization to interacting fields is also possible?
In the interacting ...
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1
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Is the symmetry of a system self-adjoint?
Say we have the statement;
An observable $A$ is a symmetry of the system if $[A,\hat H]=0$ where the Hamiltonian doesn't explicitly depend on time.
We now know that $A\hat H = \hat H A$
does this ...
7
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0
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251
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Feynman rules from LSZ reduction formula in theories with derivative couplings
I am trying to compute the Feynman rules for a theory with derivative coupling:
$$
\mathscr{L}_{int} = e v^{\mu} (\partial_{\mu} \phi) \phi
$$
where $\phi$ is a real, massive scalar field, and $v^{\mu}...
- 313
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1
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How to switch from the interaction picture to the Heisenberg picture?
In the Schrödinger, Heisenberg, and interaction pictures, the time evolution of an operator $A$ is defined differently.
In the $\textbf{Heisenberg picture}:$
\begin{equation}
A_H(t) = e^{i(H_0 + V)t} ...
- 288
4
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0
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77
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Twisted Operators
In higher-spin CFT, operators organize themselves into additive multi-twist. I am a bit confused as to the use of "twist-two", "leading-twist", etc. Especially when it mentioned in ...
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1
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69
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Angular momentum in Townsend QM question
I am wondering about the following statement which appears in Townsend's book on Quantum mechanics, expression (9.88), page 319.
Let $|\psi \rangle$ be some energy eigenstate. Here, $\langle \mathbf{r}...
- 43
3
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1
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302
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What is the average formula for interacting picture at positive temperature?
Although this looks a very simple question, it has been difficult to find an answer on textbooks since many of them develop the theory of interacting many particles for zero temperature and just ...
- 1,367
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What are the restrictions on the conformal dimension of a primary operator?
Consider a chiral quasi-primary field in 2D with conformal dimension $h$. Under conformal transformation it transforms as:
$$\phi^{'}(z)=(\frac{df}{dz})^{h}\phi(f(z)).$$
For the two point function of ...
- 523
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164
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Matrix element of order $n$ [closed]
Does anyone know an explicit formula to calculate the following matrix element? It is in the context of quantum optics,
$$\langle\alpha | a^n \mathcal{D}(\beta) | m\rangle,$$
where $|\alpha\rangle$ is ...
2
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How can I find the value of lambda from these two equations?
The Hilbert space is $\mathcal{H} = \mathcal{H}_q \otimes \mathbb{C}^2$.
A general spinor $\Phi \in \mathcal{H}$ is
$$
\Phi =
\begin{pmatrix}
\alpha \\
\beta
\end{pmatrix}
=
\begin{pmatrix}
\...
1
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1
answer
109
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Lindblad operators in a composite system
Consider a qubit described by a Hilbert space with basis vectors $|0\rangle$ and $|1\rangle$. The system undergoes spontaneous decay, modeled by a master equation in Lindblad form with a Lindblad ...
- 127
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128
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Basis of states, and matrix representation
If there is a quantum state, like a wave function, how do I know in which basis should I write it should I choose the basis, for example for the hydrogen atom what ...
2
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1
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737
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What does the notation in Sakurai's text mean?
I'm trying to understand Sakurai's explanation leading up to the projection operator, pp. 17-18 (Section 1.3.2), but I'm slightly confused by the notation. So he first says that an arbitrary ket $|\...
- 153
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258
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Do quantum entities lack definite positions because of measurement limits, or is it a fundamental feature of nature? [duplicate]
In quantum mechanics, particles such as electrons do not have a fixed position until they are measured
Questions:
Is this indeterminacy simply due to the limitations of our current measurement ...
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1
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164
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Derivation of expressions for $\langle\hat{p}\rangle$ and $\langle \hat{p}^{2}\rangle$ in quantum mechanics: Where am I making a mistake? [closed]
Suppose $\psi(x)$ is a properly normalized wavefunction of a particle. By definition we have that $\left<x|\psi\right> = \psi(x)$. The definition of the momentum operator (along $x$) is $\left&...
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About the compactification radius of compact bosons under fields redefinition
I am having trouble understanding the compactification radius of compact bosons under redefintion of the fields.
Suppose we have two compact chiral bosons with period $\phi_R \sim \phi_R +2\pi$ and $\...
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0
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24
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Defining or Listing Measurable/Observable quantities [duplicate]
In Quantum Mechanics, certain quantities are considered to be "measurable" or "observable". We demand the following properties of these quantities:
They must be real
They must be ...
2
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0
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130
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Wick contraction in CFT
I am reading Tong's lecture notes on CFT and I can't reproduce a result at pag. 82
$$T(z):e^{ikX(w)}:=-\frac{\alpha'^{2}k^{2}}{4}\frac{:e^{ikX(w)}:}{(z-w)^{2}}+ik\frac{:∂X(z)e^{ikX(w)}:}{z-w}+...\tag{...
- 783
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131
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Complex conjugate of a fermion creation operator
I am analyzing page 70 of Peskin & Schroeder concerning the complex conjugate, where in Eq. (3.145) they write the following:
\begin{equation}
\begin{split}
-i\gamma^2 \int \frac{d^3p}{(2\pi)^3} \...
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