Questions tagged [notation]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
1answer
77 views

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....
0
votes
0answers
50 views

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 ...
1
vote
2answers
220 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{\...
0
votes
2answers
141 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 $M$ ...
0
votes
1answer
161 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
votes
1answer
119 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| ...
2
votes
0answers
37 views

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 ...
0
votes
3answers
103 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 \...
1
vote
0answers
23 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 ...
1
vote
1answer
69 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 $L$?
0
votes
2answers
53 views

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: $$...
0
votes
2answers
761 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} ...
3
votes
2answers
591 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
votes
2answers
156 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
vote
1answer
85 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 ...
1
vote
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
votes
1answer
62 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 ...
0
votes
0answers
21 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
vote
1answer
155 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 ...
0
votes
3answers
180 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
vote
1answer
224 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
vote
1answer
94 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
votes
1answer
80 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 ...
0
votes
1answer
58 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? ...
1
vote
1answer
36 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], ...
-1
votes
1answer
61 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 ...
0
votes
1answer
49 views

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 $\...
1
vote
2answers
100 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 \...
3
votes
1answer
359 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
votes
1answer
164 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 $N$ ...
0
votes
1answer
80 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 ...
1
vote
1answer
129 views

Simple explanation of a particular diagrams of Feynman [closed]

In relation to this question posed on the website TeX.SE. I am curious to know the use in Physics of green functions about the signs of feynman diagrams with fermionic fields. I have not understood ...
-1
votes
1answer
51 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 ...
3
votes
2answers
118 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}(...
0
votes
0answers
89 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)
0
votes
1answer
54 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,...
3
votes
1answer
43 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
votes
1answer
85 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 ...
1
vote
1answer
195 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/...
2
votes
1answer
192 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 = | ...
0
votes
1answer
43 views

What do $I_{x2}$ and $I_{x3}$ represent in this Circuit? [closed]

I thought it would be Ix2 = I2 or Ix2 = 2I2. if that makes sense. The question asks for Voltage across R2 but i dont want an answer, i just need to know what those two symbols stand for so i can get ...
1
vote
2answers
66 views

When is the order of magnitude not equal to the exponent of scientific notation?

Explain why the order of magnitude is sometimes not the same as the exponent in scientific notation. It is because of the units?
0
votes
0answers
60 views

Mathematical representation of Symmetry Transformation

Consider a general Hamiltonian that is made up of three terms $\mathcal{H}$ = term I + term II + term III . Suppose the combination of charge conjugation and parity (CP) is a symmetry of this ...
6
votes
3answers
212 views

What exactly is $\langle x |$?

It's a linear functional, but what exactly does it do? It maps a wavefunction $|\psi \rangle$ to an element of $\mathbb C$, but what.. exactly does that mean? I know heuristically it maps $\psi$ to ...
1
vote
0answers
31 views

Notation in a question on probabilities and particle counting

I'm working through Stephen Barnett's book on quantum information and have come across the following question (1.5, for anyone keeping track at home) A particle counter records counts with an ...
0
votes
2answers
152 views

How does 4-vector notation work?

In particle physics we are going over 4-vector notation. However, my background on this is a little shaky, and I'm having difficulty differentiating the notation and visualizing what it actually means....
0
votes
3answers
134 views

Some confusions about Navier-Stokes equations

I just started working on the Navier-Stokes equations. I consider the following paper Seibold A compact and fast Matlab code solving the incompressible Navier-Stokes equations on rectangular domains (...
1
vote
3answers
95 views

Difference between $\bf J$ and time derivative of $\bf E$ in Maxwells equations? [closed]

Maybe I am being confused. It was some years ago I did this. An electric current changes charge distribution which creates rotation in $\bf B$. So in Ampères / Biot-Savarts law what is the difference ...
1
vote
2answers
153 views

Gauge-covariance of the Yang-Mills field strength $F_{\mu\nu}^a$

Accordingly to Yang-Mills theories, after the introduction of a covariant derivative such that $$D_\mu = \partial_\mu - igA_\mu, \tag1$$ you can built the kinetic term for the gauge potential $A_\...
1
vote
1answer
63 views

Math notation for heating object

An object with mass $m$ and heat capacity $c_{p}$ is exposed to heating $P_{th} $[kW] and thermal losses $\dot q$ [kW/°C]. The energy equation illustrating the process of heating it from $T_{max}$ to $...