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Questions tagged [notation]

This tag is for questions on the meaning, history, and usage of various symbols and notation that are used to denote different quantities in physics. Don't forget to mention the reference, where you encountered those notations.

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Operator's definition in Dirac picture [closed]

I have a question about the definition of quantum operators in the Dirac picture. The definition is: $$A=\sum_i \sum_j \vert i \rangle A_{ij} \langle j \vert.\tag{1}$$ By deplacing the ket vector I ...
Dayane's user avatar
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1 vote
5 answers
106 views

What does it mean when vector quantity is negative?

I’ve seen in some problems that vector quantity is negative. For example, negative Coulomb means that two charges attract… negative acceleration means that object is slowing down. However, magnitude ...
Alexander Djurovich's user avatar
0 votes
1 answer
76 views

What does $v$ actually represent in pulley problems?

Let us consider the problem of two pulleys with boxes attached to their ends. One pulley is movable, and the other is not. The problem requires us to find a relationship between velocities of these ...
Alexander Djurovich's user avatar
1 vote
0 answers
40 views

About the notation for TEM waves

I just came across this article where the term "$\mathrm{TE}_{101}$ microwave mode" is mentioned. Other than the basics of TEM waves which I learned in Griffiths, this is the first time I ...
hendlim's user avatar
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0 votes
1 answer
144 views

What's the difference? $\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$

What's the difference? $$\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$$ In John Dirk Walecka's book 'Introduction to General Relativity',...
Jianbingshao's user avatar
-1 votes
0 answers
19 views

How to state that a function has a certain andament in a limit? [migrated]

Assuming we have a function $f(r)$ that has the following limit $$ \lim_{r\to0} f(r) = \frac{5}{3 r^2} \,.$$ What is the correct symbol to express that the denominator goes like $r^2$? Is the ...
Aleph12345's user avatar
-2 votes
1 answer
127 views

Multiplication of $\mathrm{U}(3)$ matrices [closed]

On this page of this paper: I am unable to understand how they multiplied the $3\times 3$ $\mathrm{U}(3)$ matrix with $T_{3,2}$, which is a $2\times 2$ matrix, in Eqs. (26) to (28). Can anyone please ...
shome's user avatar
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1 answer
102 views

What does the superscript $3$ in $d^3x$ mean in an integral?

At the risk of seeming ignorant, please explain what does the superscript $3$ in $d^3x$ mean in the integrals 5.12, 5.13, 5.14, 5.15? Why 3? Why there is no such in the 5.10 integral?
question-asker's user avatar
0 votes
2 answers
65 views

What is $r$ in a metric signature in general relativity? If $v$ and $p$ are the time and spatial coordinates?

The Wikipedia article on metric signatures says that the signature of a metric can be written $(v,p,r)$, where $v$ is the number of positive eigenvalues, $p$ is the number of negative eigenvalues, and ...
Kurt Hikes's user avatar
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1 vote
2 answers
128 views

Would it be valid to say $y \propto 2x$ instead of $y \propto x$?

Would it be acceptable to write $y \propto 2x$ or would it be wrong to add the $2$? I just want to describe a relationship in more detail.
Yifan YIN's user avatar
0 votes
2 answers
76 views

Questioning the Probability Expression for Neutrino Oscillation in Griffiths' "Introduction to Elementary Particles"

In Griffiths' book, Introduction to Elementary Particles (Griffiths, D. (2020). John Wiley & Sons, p. 390), the author defines the pure electron and muon neutrino states as: $$|ν_{e}\rangle=-\sinθ|...
Okba's user avatar
  • 67
2 votes
0 answers
72 views

What is the meaning of the tensor product ($\otimes$) of groups? Is is the same as the cartesian product ($\times$)? [duplicate]

In the high energy physics literature and in some discussions on group theory for physics, the tensor product $\otimes$ of groups is sometimes mentioned. For example, the gauge group of the standard ...
Aqualone's user avatar
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0 votes
1 answer
42 views

Index notation for the generalized form of the velocity gradient with shear and rotation

Good day guys, I was studying fluid dynamics and came across the following equations (shown in the image): When we have both shear and and rotation, they each contribute to the change in velocity ...
STOI's user avatar
  • 286
-1 votes
1 answer
76 views

What does the notation $d𝜏'$ mean?

$\text{I was studying helmotz theorem and saw this notation, what does it mean? How is d}\tau' \, \text{ different from d}\tau \text{?}$ From :- David J. Griffiths-Introduction to Electrodynamics-...
DocAi's user avatar
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4 votes
3 answers
110 views

Complex coordinates $ds^2 = dzdz̄$ in 2d

I have a very elementary question about complex coordinates in two dimensions. When we have a 2D Euclidean space, $$ds^2 = dx^2 +dy^2$$ and we go to complex coordinates: $$z = x + iy$$ $$z̄ = x - iy$$ ...
j_stoney's user avatar
0 votes
0 answers
90 views

Component notation and matrix notation for gradient of vector

I'm trying to understand vector and tensor notation, but I'm coming across some difficulties. Say I have vector $\vec{u}$ and I compute its gradient $\nabla \vec{u}$. Then I get a tensor $\frac{\...
John Vector's user avatar
-1 votes
1 answer
52 views

Coordinate-free calculations in bra-ket notation [closed]

I'm interested if bra-ket notation can be used without having to introduce a basis or coordinates in calculations and proofs. For example, could the notation, if need be, extended with some exterior ...
Gauge's user avatar
  • 93
0 votes
0 answers
19 views

Integration over the complex plane and the completeness relation of the coherent states [duplicate]

I am studying some of the properties of coherent states using the book "Introductory Quantum Optics" by C. Gerry & L. Knight. (C. Gerry & L. Knight, Chapter 3, Section 5) And when I ...
Uriel Casco D's user avatar
0 votes
0 answers
31 views

Understading dimensions in quark bilinears

I have encountered myself with the following definition for $\pi$-fields as quark bilinears: $$ \pi^a = i\bar{q}\tau^a \gamma_5 q \ ,\quad\text{with }\ q = \left(\begin{array}{c}u\\d\end{array}\right) ...
SrJaimito's user avatar
  • 601
0 votes
1 answer
107 views

Mathematical meaning of a position eigenbra $\langle x_0 |$

Let $|x_0\rangle$ be an position eigenket. The physical picture I have for $|x_0\rangle$ is a particle located at $x_0$. Thus it should be represented by a delta function $\delta(x-x_0)$. For $f\in L^...
CBBAM's user avatar
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0 votes
1 answer
84 views

Can unit prefixes be interpreted as algebraic stand-ins?

I am currently a little confused about whether unit prefixes can be interpreted algebraically For example: $$4km = 4\times 10^{3} m$$ Is it incorrect to say that $k$ is simply an algebraic stand in ...
cookiecainsy's user avatar
0 votes
1 answer
35 views

Question about meaning of "bar"-ing in the context of Dirac fields

Following chapter 38 of Srednicki, "bar"-ing means (based on eq. 38.15) $$\bar{A} = \beta A^\dagger\beta$$ One can show for instance that $$\bar{\gamma^\mu} = \gamma^\mu$$ My question is, ...
JohnA.'s user avatar
  • 1,713
2 votes
2 answers
343 views

Orthogonality of Lorentz transformation [duplicate]

I know this might be a general or well known topic, but please bear with me, since I have a very specific question regarding this and I want to see specifically whether there is a flaw in my reasoning ...
Stallmp's user avatar
  • 665
-4 votes
1 answer
64 views

What is the effect of the operator $\hat{O} = |\phi \rangle \langle \psi|$ on any state $| \psi \rangle$? [closed]

I have seen this operator in some questions,including the book Liboff,Introductory Quantum Mechanics. I am not sure how it would act on a state.
blackholesandrevelations's user avatar
0 votes
1 answer
63 views

Raising and lowering indices of Kronecker delta [duplicate]

I have some confusion about how to raise the indices of the Kronecker delta. To raise and lower indices we use the metric tensor, let's suppose to use the metric (+---). I should have that $$g_{\mu\nu}...
Michael 's user avatar
-1 votes
2 answers
126 views

Why do we multiply the Euler-Lagrange equations by negative one?

As I've learned classical mechanics from different sources, I've seen both $$\frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}_k} \right) - \frac{\partial L}{\partial q_k} = 0,$$ and $$\frac{\...
wlancer's user avatar
  • 183
1 vote
2 answers
100 views

Directional derivative $(\mathbf{A}\cdot\nabla)\mathbf{B}$ of the vector field $\mathbf{B}$

While reading Introduction to Electrodynamics by David J. Griffiths, I have encountered some issue with the notation of the directional derivative of the vector field and I was wondering if there are ...
Tomasz P's user avatar
0 votes
2 answers
98 views

Einstein Summation Convention Confusion

My textbook: The second bit confuses me. I asked a question on this site yesterday (Moment of Inertia tensor confusion) which involved the moment of inertia tensor and the term $$r_{i}r_{j}$$ The ...
ED2468's user avatar
  • 75
5 votes
4 answers
916 views

Contracting the metric tensor with its inverse yields Kronecker delta

It's probably straightforward, but I would like to see the proof of the identity: $$g_{\mu\nu}g^{\nu\alpha}=\delta^\alpha_\mu.$$ In the book 'Spacetime and Geometry' by Carroll, this identity is the ...
ceciled's user avatar
  • 71
0 votes
1 answer
51 views

Moment of Inertia tensor confusion

This is the moment of inertia tensor about the COM. $$I_{ij}'=\sum_{k=1}^Nm_k\left[\vert\mathbf{r}'^{(k)}\vert^2\delta_{ij}-r_i'^{(k)}r_j'^{(k)}\right]\neq I_{ij}$$ I don't understand how to compute ...
ED2468's user avatar
  • 75
0 votes
0 answers
40 views

In diagrams, how can I indicate that a body is not moving or rotating?

I often create diagrams to illustrate the scenario of an exercise for my students. These are not necessarily free-body diagrams, as creating those may be part of the task or similar or it would be ...
Wrzlprmft's user avatar
  • 6,294
5 votes
3 answers
2k views

Where does the negative sign disappear?

The defining equation for simple harmonic motion is such $$a=-ω^2x$$ When we find the centripetal acceleration of an object in orbit we use the formula $$a=ω^2r$$ As a consequence of the accleration ...
Quin Gardiner Bax's user avatar
1 vote
1 answer
109 views

Showing the Variance of an observable in a determinate state is always zero

I am working through Introduction to Quantum Mechanics by David J. Griffiths, and part 3.2.2 shows that the standard deviation of an obervable, $Q$, is always $0$ but I do not understand the steps ...
cookiecainsy's user avatar
0 votes
2 answers
46 views

Notation for intrinsic charge carrier

What exactly is $n_{\textrm{i}}$? It is said to be the intrinsic charge carrier, but for pure semiconductors, $n_{\textrm{h}} = n_{\textrm{e}} = n_{\textrm{i}}$, is $n_{\textrm{i}}$ not the sum of ...
ishigami's user avatar
7 votes
5 answers
1k views

What is the distinction between a ket and a state in quantum mechanics?

Sorry if this has been asked before in some manner, but I'm just a bit confused about the distinction between a state $\alpha$ and its ket $|\alpha\rangle$. I was recently told that a state $\alpha$ ...
Pedro Hablespanyos's user avatar
0 votes
0 answers
81 views

How to draw topological defect line in LaTeX?

This is somewhat between TeX stackexchange and physics stackexchange. With Latex, it became much more easier to write equations, and with tikz, pictures can be drawn. However, with the introduction of ...
ShoutOutAndCalculate's user avatar
1 vote
1 answer
111 views

Feynman slash identity

How would one simplify the expression $\gamma^0 {\not}p \;\gamma^0$ ? My guess would be that its $$\begin{align} \gamma^0 {\not}p \;\gamma^0&=\gamma^0 \gamma^{\mu} p_{\mu} \;\gamma^0\\ &=\...
MVPlanet's user avatar
2 votes
2 answers
115 views

Notation for spatially superposed particle using vacuum modes - Why the state of the particle and vacuum is entangled, not separable?

We have two places, call them Here and There where a particle could be. When the particle isn’t spatially superposed we write its state as $ |1\rangle_{Here}\otimes|0\rangle_{There}$ zero being the ...
Sutasu's user avatar
  • 21
1 vote
0 answers
58 views

What is a "reciprocal ordering" when discussing quasiprobability distributions?

The Wikipedia page about the optical equivalence theorem mentions that, if we denote with $f_{\Omega}(\hat a,\hat a^\dagger)$ an "operator that is expressible as a power series in the creation ...
glS's user avatar
  • 14.8k
3 votes
2 answers
200 views

Clarification about Wald's notation on his General Relativity Book

In equation 4.1.4 Wald describes the metric in pre-relativistic physics as, $$h_{ab} = \sum_{\mu, \nu} h_{\mu\nu}(\mathrm{d}x^{\mu})_a (\mathrm{d}x^{\nu})_b\tag{4.1.4}$$ with $h_{\mu\nu} = \mathrm{...
Jeff's user avatar
  • 221
0 votes
1 answer
74 views

What does the notation $(k \cdot \nabla ) v$ mean? [duplicate]

I am reading a paper and it uses a notation I am not too familiar about. Although I saw it used elsewhere, I don't remember the meaning of it and I don't want to misinterpret it and realize after ...
tommy1996q's user avatar
0 votes
0 answers
66 views

Commutation of the operators used in definition of dispersion in Sakurai's proof of uncertainity [duplicate]

Given a Hermitian operator $A$, Sakurai (in his book "Modern Quantum Mechanics") defines $\Delta A$ as follows: $$\Delta A = A - \langle A\rangle$$ Where I believe $\langle A\rangle\vert\psi\...
SweepingBishops's user avatar
2 votes
1 answer
120 views

Columns, rows, dotted, undotted, $SL(2, \mathbb{C})$ reps, and building Dirac spinors from Weyl spinors

I'm looking through Introduction to Supersymmetry by Muller-Kirsten and Wiedemann, along with any other resource I can find. I'm specifically trying to understand the concepts and notations for ...
Gleeson's user avatar
  • 213
-2 votes
2 answers
59 views

Can the different differentiation notations be equated and do they have an integral definition? [closed]

Are these all equivalent and is there an extension of this to other notation? Does anyone have a clear and concise chart equating the different notation dialects? I am also curious if there are more ...
Kenneth Mikolaichik's user avatar
2 votes
2 answers
584 views

Change of basis in bra-ket notation [duplicate]

In the post Change of Basis in quantum mechanics using Bra-Ket notation , the accepted answer explores the relationship between an arbitrary operator $\hat{x}$ and another named $\hat{u}$, such that $\...
JBatswani's user avatar
  • 187
0 votes
1 answer
90 views

Integral expansion of a ket [closed]

I'm taking my first quantum physics course and I've been seeing a lot of stuff like $|\psi\rangle = \int d\phi |\phi\rangle \langle \phi | \psi \rangle$ and $|\psi\rangle = \int d^3 r |r\rangle \...
JBatswani's user avatar
  • 187
0 votes
1 answer
39 views

Abbreviations for energy and torque

What are correct abbreviations for torque and energy in US Customary and S.I. systems? Both include distance and force. Do we write N-m and lbf-ft for both torque and energy? I always heard (years ago)...
Bill's user avatar
  • 79
1 vote
2 answers
80 views

Why we use $ΔQ$ in thermodynamics if heat $Q$ is flow of energy? (What's difference are we calculating here?)

If I think heat as transfer of energy from hot body to cold body, how I calculate difference $\Delta Q$. Shouldn’t $Q$ be used instead?
Himalayan's user avatar
2 votes
1 answer
110 views

Why are these two forms for an operator equivalent?

According to a paper I am reading (https://arxiv.org/abs/1904.08448. roughly page 8), an operator $K(t)$ is define as follows: $$ K(t) = i\hbar\sum_n | \dot{n}_0(t)\rangle \langle n_0(t)| \tag{1} \...
Idieh's user avatar
  • 71
3 votes
2 answers
249 views

Neutral Hydrogen Atom Time-Averaged Potential

I'm self-studying the 3rd edition of Jackson's Classical Electrodynamics and I have a question about a problem. The fifth problem of Chapter 1 asks the reader to determine the volume charge ...
kandb's user avatar
  • 373

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