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Questions tagged [notation]

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2answers
36 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
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2answers
61 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
506 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 ...
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2answers
42 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 ...
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1answer
74 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
23 views

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

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?
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1answer
46 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 ...
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0answers
48 views

Infinitesimal squared in metrics [migrated]

Metrics are often formulated by appealing to the square of an infinitesimal quantities. Examples of such are: $$ (ds)^2=(dx)^2+(dy)^2 $$ or $$ ds^2=dx^2+dy^2 $$ or $$ d(s^2)=d(x^2)+d(y^2) $$ ...
2
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1answer
141 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
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3answers
121 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
48 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 (...
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1answer
60 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
51 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
26 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
31 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
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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
36 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 $\...
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2answers
73 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 \...
1
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1answer
63 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
44 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
63 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 ...
0
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1answer
37 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 ...
4
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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
49 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
46 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
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1answer
34 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
49 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
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1answer
22 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
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1answer
79 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
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1answer
42 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 ...
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2answers
58 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
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0answers
56 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 ...
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3answers
201 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
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0answers
26 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 ...
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2answers
89 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
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3answers
104 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 (...
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3answers
75 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 ...
0
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2answers
80 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
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1answer
62 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 $...
0
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1answer
25 views

Faraday's Induction Law Notation

I am confused as to the notation used in a course I'm taking on physical optics. I have presented 2 variants of Faraday's Law, combined with the full set of Maxwell's equations. The first ...
0
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2answers
87 views

Notation and concepts of Yang Mills Theory

I am studying loop quantum gravity using the book by Pullin and Gambini. I am having some trouble understanding and getting past the chapter on Yang Mills theory, mainly because I am confused about ...
0
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2answers
55 views

Scientific notation and usage thereof [closed]

I'm taking my first physics exam in university this Saturday, and I'm currently working on a practice exam. I got the answer 3.1MeV for a alpha-decay question, but the answer was 3100keV. I ...
0
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5answers
100 views

Confusion about ket states and bra with position

I am very confused about the bra-ket notation of states and the fact that $$\psi(x) = ⟨x|\psi⟩$$ and $$⟨x|x'⟩ = \delta(x-x')$$ are true. What does this mean? What is the ket $|x⟩$, is it just some ...
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2answers
128 views

Would a commutative power operator simplify some equations of physics? [closed]

Hypertype Theory makes the radical suggestion that a commutative power operator would be preferable to the traditional non-commutative power operator $a^b$. Are there any equations in physics that ...
3
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5answers
228 views

Why isn't there a minus sign in Ohm's law, $V = IR$?

Suppose current runs through a resistor from left to right, and we define the left-to-right direction as positive. Then from left to right, the potential decreases. So $V,$ the voltage across the ...
2
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1answer
62 views

How is the complex integration done for the Wigner function in coherent state representation?

$$W(\alpha)=\frac{1}{\pi^2}\int e^{\lambda\alpha^*-\lambda^*\alpha} \operatorname{Tr}\left[ \hat{\rho}e^{\lambda\hat{a}^\dagger} e^{-\lambda^* \hat{a}} \right] e^{-\frac{|\lambda|^2}{2}} \, d^2\lambda....
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2answers
127 views

Representing tensor products using Dirac's bra-ket notation

I know, that $$ \uparrow \equiv \left[ \begin{array} { l } { 1 } \\ { 0 } \end{array} \right] $$ and $$ \bigg| \frac { X - i Y } { \sqrt { 2 } } \bigg \rangle = \sqrt { \frac { 3 } { 8 \pi } } \frac { ...
1
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1answer
73 views

How to differentiate Capacitance (Italized C) and Coloumbs (regular C) on paper [closed]

I am doing a question on capacitance and coulombs. I got the answer correct, but I was wondering how a physicist, when doing the calculation on paper, would differentiate a C and C?
1
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1answer
40 views

Peskin and Schroeder: derivation of Dirac fields commutator

I'm perplexed by the following non numbered equation at page 54 of Peskin & Schroeder, right between $(3.92)$ and $(3.93)$ $$ [\psi_a(x),\overline{\psi}_b(x)]=\int\frac{d^3p}{(2\pi)^3}\frac{1}{...