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Questions tagged [notation]

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1answer
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Why the $L$ in an $RLC$ circuit? [duplicate]

I was studying for a differential equations class and came upon some information about $RLC$ circuits. I know the $R$ stands for resistance (makes sense) and $C$ stands for capacitor (this also makes ...
1
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1answer
62 views

What does the notation $\langle a|b|c\rangle$ mean? [on hold]

What does the notation $\langle a|b|c\rangle$ mean? I saw this in a Quantum Mechanics book and couldn’t understand it
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0answers
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Where does this alternative form of Faraday's law come from?

In the Sears-Zemansky physics book on page 1007, there is an alternative way to express Faraday's law for a moving conductor in a magnetic field: $$d\mathcal E =\left(\vec v \times \vec B\right)\cdot ...
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0answers
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Applying the adjoint of an operator

Consider the following inner product: $$ \langle x | Z\rho Z^\dagger | y\rangle$$ Here $Z$ is an operator and $Z^\dagger$ is it's conjugate. $\rho$ is a density matrix. Does this equal to the ...
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0answers
56 views

Why do particle physicists often use $\otimes$ instead of $\times$ to denote the direct product of groups? [closed]

For example, sometimes one sees $SU(3)\otimes SU(2)\otimes U(1)$ instead of $SU(3)\times SU(2)\times U(1)$. My understanding is the the product here is just the usual direct product (aka Cartesian ...
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1answer
84 views

Tensor index in special relativity?

I'm studying special relativity and I have some difficulties with tensor index. Take for example the Lorentz matrix, whose elements are written as $\Lambda^\mu{}_\nu$. $\Lambda^\mu{}_\nu(v) = \...
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3answers
77 views

What does $X|n\rangle \propto |n+c\rangle$ mean?

$\renewcommand{\ket}[1]{\left \lvert #1 \right\rangle}$ I'm transcribing below (but see edit history for a scan) a calculation from pg 17 of this article on Lie groups and Lie algebras $$ [N,X]=cX....
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1answer
66 views

Confusion Einstein notation polar coordinates

I'm having issues using Einstein notation in polar coordinates in flat space, I must be missing something basic. Consider the following example. Take the following metric on a 2+1 spacetime; $ds^2 = ...
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1answer
49 views

Question about commutators acting on wavefunctions

Consider a commutator acting on a 1D wavefunction: $$[\frac{\hbar}{i} \frac{d}{dx},x]\psi(x)=(\frac{\hbar}{i} \frac{d}{dx}x-x\frac{\hbar}{i} \frac{d}{dx})\psi(x).$$ Now does this mean $\frac{\hbar}{...
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1answer
50 views

$\delta^{(2)}$ convention

In this note: https://arxiv.org/abs/hep-th/0410165 at page 12 there is a delta-function constraint written as: \begin{align} \delta \left( ^ { U } M \right) = \prod _ { i < j } \delta ^ { ( 2 ) } \...
2
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1answer
35 views

Arrow convention for neutral particles in Feynman diagram

In a Feynman diagram, the arrows on the charged particles are along the direction of negative charge flow. As a result, the arrow is not always directed from the vertex of creation and not always ...
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1answer
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Vector calculus notation, maybe?

I just got a new book on turbomachinery that uses some notation I'm not familiar with. $$ \nabla \lor \vec{W} = -2\vec{\Omega} $$ The del-(something)-vector format makes me think its vector calculus....
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How to understand notation in “Introduction to Quantum Mechanics (3rd Edition)” by David Griffiths, Chapter 3.6.2?

In the 3rd edition, on page 118, the projection operator is introduced as $$\hat{P}=|\alpha\rangle\langle\alpha|.$$ Then Griffiths says that when $\hat{P}$ acts on another vector, it looks like ...
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1answer
50 views

Convective derivative vs total derivative

I was wondering what is the difference between the convective/material derivative and the total derivative. We were introduced to the notion of material derivative $$ \frac{D\vec{u}}{Dt}=\frac{\...
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2answers
120 views

What does “$\gg$” mean in physics problems?

In the context of this: Our goal in this subsection will be to obtain $r$ as a function of $θ$, for a gravitational potential. The gravitational potential energy between two objects, of masses $M$ ...
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1answer
52 views

Matrix representation of spin-1/2 operators in Sakurai

Hello and thanks for reading. I'm an undergrad working through the first chapter of Sakurai's text and was going through the principles of the spin-1/2 system. The author demonstrates closure and ...
2
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1answer
69 views

Asymptotic LSZ reduction formula (Peskin & Schroeder)

Peskin & Schroeder, An Introduction to Quantum Field Theory, write at page 224 $$\int d^{4} x e^{i p \cdot x}\left\langle\Omega\left|T\left\{\phi(x) \phi\left(z_{1}\right) \cdots\right\}\right| ...
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0answers
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Notation for the vector space of (real) classical solutions

I am aware that this might not be the best place to ask, but I can't say I know of any other better alternative so I apologize in advance. I'm following Wald's book on QFT in curved space-time and I ...
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3answers
90 views

Confused about defining $\psi(x)=\langle x|\psi\rangle$ in Dirac notation

I'm reading Shankar QM and in chapter 11.2 Eq. 11.2.7, he uses the projection operator (summed over infinity) to project the $|\psi\rangle$ state in the $x$-basis as follows: $$ \int |x\rangle \...
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0answers
20 views

Different between index locations on tensors

My question is in regard to the position of upper and lower indices on tensors, specifically in this case I am considering position 4-vectors and the Minkowski matrix. On the Wikipedia page I see ...
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1answer
65 views

Is there a historical name for an inductor that starts with the letter $L$? (RL circuits) [closed]

Why is a circuit with a resistor and inductor called an RL circuit and not an RI circuit? Was there a now-obsolete name for an inductor that started with the letter $L$?
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2answers
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Anti-symmetrization brackets break Einstein summation convention

How does one properly evaluate something of the form $$ g_{a}^{\, [b} R_{c] b}~? $$ when I try to expand using the definition of anti-symmetrization brackets the Einstein summation seems to break: $$...
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2answers
131 views

Inverse of metric tensor

The Minkowski metric tensor have the relation $\eta_{ij} \eta^{jk}=\delta_i {^k}$. That is the inverse of the Minkowski matrix is the matrix itself. Analogously, is it true that $g_{ij} ...
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2answers
542 views

Integral Notations in Quantum Mechanics [duplicate]

I've been learning about Quantum Dynamics, time evolution operators, etc. I am confused about the notation used in integrals. Normally I am used to integrals written in this way (with $dx$ on the ...
4
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2answers
87 views

Can the Hamiltonian operator act on a bra, if it was once acting on a ket?

I was watching a MIT Quantum Physics III class when I got a doubt about a specific bra-ket manipulation. My doubt is about the step from the expression $(3.7)$ to the expression $(3.8)$ of the lecture ...
1
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1answer
76 views

How to simplify this expression in Dirac notation

An expression cropped up in a homework problem that I'm not sure how to simplify. Consider the following, where $|x\rangle $ is a position eigenstate and $|p_1\rangle, |p_2\rangle$ are momentum ...
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0answers
25 views

Why is angular velocity in LCR circuits denoted by ω'? [closed]

This might be a dumb question, but I was wondering why the omega denoted in LCR oscillations ω' instead of just ω. Is it that ω' is the derivative of ω or is it just a notation?
0
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1answer
49 views

Eigenstates of position in Schrödinger picture

Hallo I'm trying to understand the concept of representation in the position space. I read that $|x\rangle$ are the eigenstates of the position operator, but I think this states should evolve in time ...
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0answers
8 views

Spectroscopic notation for $As$

I’m wondering if I’m approaching hund’s Rules for Arsenic correctly (Ar): (Ar)$(3d)^{10}(4s)^{2}(4p)^{3}$ I started with HR1: Maximize the spin. I have 6 orbitals so I can put one electron in the ...
1
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1answer
148 views

What does $|$ mean in the Schrödinger Equation?

I saw the $|$ symbol in the Schrödinger Equation $$i\hbar\frac{\partial}{\partial{t}}|\Psi(r,t)\rangle=\hat{H}|\Psi(r,t)\rangle$$ But I don't know what the $|$ means. What does $|$ mean in the ...
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3answers
132 views

Understanding Einstein notation in special relativity

I'm entering the realm of special relativity and amazingly the hardest part about it is the notation! I'm confused on exactly how to intuitively build an understanding, and this may be hindering the ...
1
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1answer
87 views

Notation for the divergence of a rank 2 tensor

I am studying advanced fluid mechanics and sometimes you see equations written in index notation like $$ Dv_i= \partial_t v_i +v_j\partial_jv_i$$ but sometimes you find this arrow/vector notation (...
1
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1answer
75 views

What is the meaning of $d$? [duplicate]

What is the meaning of $d$? Is is Delta? If it is Delta, why is it then not $\Delta$? I am still confused with that. Can someone help explain it to me?
0
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1answer
56 views

Tensor Derivatives in Index Notation in Special Relativity

The energy-momentum tensor $T^{\mu\nu}$ is not uniquely defined because we can add a term $\partial_{\lambda}X^{\lambda\mu\nu}$ to it, where $X^{\lambda\mu\nu} = - X^{\mu\lambda\nu}$, and show that it ...
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1answer
37 views

Square bracket notation of the basis of 16 independent gamma matrices

The question is very simple and I couldn't find an answer. What the notation $\gamma^{ [ \mu} \gamma^{\nu} \gamma^{\rho ]}$ and $\gamma^{ [ \mu} \gamma^{\nu} \gamma^{\rho} \gamma^{\sigma ]}$ means? ...
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1answer
34 views

Question about explicit notation of averaged energy conditions integrals

Beyond the basics of general relativity, we rapid encounter the so called Averaged energy conditions. The mathematics of these quantities are related to line and volume integrals. As given by [1], ...
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1answer
59 views

What is the meaning of the notation $\langle a_1, \ldots, a_n \mid X_i(u) \mid a_1', \ldots, a_n' \rangle$? [closed]

I am from the math department and reading Belavin & Gebner's On the Algebraic Approach to Solvable Lattice Models. I am trying to understand the left-hand side of Equation (2.2) on page 4. What ...
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1answer
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What does the notation of the subscript behind the brackets in the differential mean?

From "Theoretical Mechanics of Particles and Continua" by A. Fetter and J. Walecka. As emphasized in the preceding section, the general expression $(7.11)$ can be applied to the coordinate vector $\...
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2answers
79 views

Reason why dot notation isn't used for time derivatives in Maxwell's equations [closed]

Maxwell's equations seem to be usually written: \begin{align} \nabla \cdot \mathbf{E} &= \rho/\epsilon_0,\\ \nabla \cdot \mathbf{B} &= 0,\\ \nabla \times \mathbf{E} &= -\frac{\partial \...
2
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1answer
113 views

Lagrangian of Klein Gordon equation

Consider the following Lagrangian density $$ \mathcal{L}(\Phi,\partial_\mu\Phi)=-\frac{1}{2}\partial_\mu\Phi\partial^\mu\Phi-\frac{m\Phi^2}{2}. $$ I want to calculate the equation of motion using the ...
2
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1answer
66 views

Lagrange equations in a conservative system, understanding $\nabla_i$

For a system of multiple particles with conservative forces: $\mathbf{F}_i = - \nabla_i V$, with $V \equiv V(\mathbf{r}_1,\dots,\mathbf{r}_N)$ the potential in function of the position of the $N$ ...
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1answer
68 views

Mass-energy equivalence - old notation

Einstein originally gave the formula as $$M = \mu + \frac{E_0}{c^2}.\tag{17}$$ In which $\mu$ was the mass of the system. Today, we more commonly get taught that the energy is in relation to the ...
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1answer
40 views

Notation for feet and inches dimension

I am looking at a set of construction plans where all the dimensions read as x' - y". One example would be 4' - 6". I am confused by the dash in between the feet and inches. Is this supposed to mean ...
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2answers
106 views

Denoting the antiderivative of velocity

With simple Newtonian laws (and in a specific context), I learned that the speed $\vec{v}$ of an object is the derivative of the corresponding position vector $\vec{OM}$. So that means that $$\vec{v}(...
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0answers
58 views

What do we mean by curly braces in an atomic configuration?

What do the '{` mean in atomic configurations e.g: 1s(2)2s(1)2p(2){3P}3p(1) 1s(2)2s(2)2p(3){4S}3p(1)
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1answer
48 views

What does the “$T$” superscript mean on vector?

My relativity book defines the "worldline" of a system as: \begin{equation} x(\tau)=(x^0(\tau),x^1(\tau),x^2(\tau),x^3(\tau))^T \end{equation} I often see velocities written in the same form: $U=(0,...
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1answer
38 views

What is $\mathbb{Z}_2$ Parity?

While reading about exotic decays of Higgs boson one of the simplest interaction that we come up with which leads to BSM decays is: $$\Delta L = \frac{\zeta}{2}s^{2}|H|^{2}.$$ This is the ...
2
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1answer
59 views

Navier-Stokes - Reynolds decomposition of energy equation

I am trying to apply the Reynolds decomposition to the Navier-Stokes equations for incompressible flows. At the moment I am doing that for the energy equation following the book Viscous Fluid Flow by ...
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1answer
56 views

What does degeneracy and multiplicity in Term symbol mean?

$^{2S+1}L_J$ was the term symbol. I watched a video online saying $2J+1$ was the fold of degeneracy to the term symbol. Specifically, for nitrogen, the term symbol for the lowest energy was $^4S_{3/...
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1answer
104 views

Orthonormal basis written in Dirac Notation

$\left\{ e _ { i } \right\}$ is an orthonormal basis which has the orthonormal condition as following: $$e _ { i } ^ { T } \cdot e _ { j } = \delta _ { i j }$$ In Dirac Notation where $| i \rangle = | ...