Notation Definition and 1000 Threads

This section of Introduction to Electrodynamics by Griffiths, section 8.2.2 (page 363), is talking about the Maxwell's Stress Tensor. I do not quite understand what the j means on the left = sign (for either of the two representations) in the attached figure highlighted in yellow color. I have...

So My Question Is Simple, But It confuse me too much! What Is Difference between the notation ∫d3x and ∫∫∫dxdydz ?

From this paper... http://pubs.acs.org/doi/pdf/10.1021/jp020363g there is a graph... Which I've been told the M means moles per litre. I now have another graph from this paper... http://pubs.acs.org/doi/abs/10.1021/jp9937407 ... Which has mM, so is this mM/L or just milli moles? Sorry for...

Homework Statement Rewrite |x| < 1 and |x| > 1 by eliminating the absolute value sign Homework Equations |x| < 1 = -1 < x < 1 |x| > 1 = ? The Attempt at a Solution I know that |x| < 1 can be rewritten as -1 < x < 1 but I'm not sure about |x| > 1. Am I right to assume that |x| > 1 = -1 > x > 1?

Hi everyone, I'm reading about the solution of the telegrapher's equations (e.g. the generalities are here https://en.wikipedia.org/wiki/Telegrapher%27s_equations ). Supposing we are treating only time t and space z, this is a second order partial differential equation on an infinite domain of...

Hi, I have a question about how to write down the following problem in a thesis. I have a standing sinusodial wave with amplitude: |\hat{q}_n| which I want to express as superposition of two traveling waves. Would you suggest do write the sum in the last line like I did, or has somebody a...

Hi all, I'm wondering if 2017-08-20T07:43:02+0000 can we tell immediately which timezone that time notation is using? so, from that one information, we can tell the exact point of time? because for example, event X happened at 15 Jul 2017 at 8.30AM, we'll immediately wonder, which timezone...

I have some questions about scalar field Lagrangians, using the box notation defined as \Box \equiv \frac{\partial^2}{\partial t^2} - \nabla^2 . It's a basic, perhaps silly issue, but somehow I've managed to sweep it under the rug for a long time. So, usually, the Lagrangian of a free scalar...

(posted in General Math in case this would be transferred elsewhere) In the thread, https://www.physicsforums.com/threads/mwi-and-path-of-single-electron.900851/page-4 someone posted: "This should be obvious; just do the same thing for subsequent measurements as we did for the initial...

I'm getting a bit confused by the specific notation in the question and am unsure what exactly it is asking here/how to proceed. Homework Statement Given a scalar function ##f## find (a) ##∫f \vec {dl}## and (b) ##∫fdl## along a straight line from ##(0, 0, 0)## to ##(1, 1, 0)##.Homework...

Hello! Does ##(x_\mu)^2## actually means ##x_\mu x^\mu## in Einstein notation?

In some sources QM is explained using bracket notation. I quite understand algebra of bracket notation, but I do not understand how is this notation related with physically meaningful things? How is bracket notation related to wavefunction notation? Could you tell me whether following is true...

Good Day Early on, in Frankel's text "The Geometry of Physics" (in the introductory note on differential forms, in fact, on page 3) he writes: "We prefer the last expression with the components to the right of the basis vectors." Well, I do sort of like this notation and after reading a bit...

I'm studying the component representation of tensor algebra alone. There is a exercise question but I cannot solve it, cannot deduce answer from the text. (text is concise, I think it assumes a bit of familiarity with the knowledge) (a) Convert the following expressions and equations into...

Homework Statement I have the following question (see below) Homework Equations The eigenvalue equation is Au = pu where u denotes the eigenstate and p denotes the eigenvalue The Attempt at a Solution I think that the eigenvalues are +1 and - 1, and the states are (phi + Bphi) and (phi-Bphi)...

Homework Statement I have a vector V with components v1, v2in some basis and I want to switch to a new (orthonormal) basis a,b whose components in the old basis are given. I want to find the representation of vector V in the new orthonormal basis i.e. find the components va,vb such that |v⟩ =...

Homework Statement I'm dealing with some pretty complex derivatives of a kernel function; long story short, there's a lot of summations going on, so I'm trying to write it down using the Einstein notation, for shortness and hopefully reduction of errors (also for the sake of a paper in which I...

I am familiar with the derivation of the resolution of the identity proof in Dirac notation. Where ## | \psi \rangle ## can be represented as a linear combination of basis vectors ## | n \rangle ## such that: ## | \psi \rangle = \sum_{n} c_n | n \rangle = \sum_{n} | n \rangle c_n ## Assuming an...

Homework Statement If I had two vectors say ⟨em|f⟩⟨f|em⟩ does this equal |⟨em|f⟩|2? e is a basis and f is some arbitrary function. I ask this because I have a problem which is to show the following: Show that for the Fourier expansion of |f⟩ in terms of Fourier basis vectors |em⟩ is...

I am reading Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with the meaning of some of the basic notation ... In talking about ways to construct field extensions Lovett writes the following on...

I am reading Abstract Algebra: Structures and Applications" by Stephen Lovett ... I am currently focused on Chapter 7: Field Extensions ... ... I need help with the meaning of some of the basic notation ... In talking about ways to construct field extensions Lovett writes the following on...

Hi. I was trying to translate the divergence theorem and the Green's theorem to tensor notation that we use in Relativity. For the divergence theorem, it was easy (please tell me if I'm wrong in the below derivation). I'm using the standard electromagnetic tensor ##F_{\mu \nu}## in place of the...

I promise that anytime I have question about Dirac notation I will ask it in this thread. I do not know how to parse the following Dirac notation. |\Psi'\rangle = |u\rangle |U\rangle Can someone please convert the Dirac notation to matrix notation?

Pronouncing a nuclear reaction like as "one,zero,neutron + 235,92,uranium yields 141,56,barium + 92,36,krypton + 3,1,0,neutron" is awkward. How is it pronounced by physicists in practice?

The Lorentz transformation matrix may be written in index form as Λμ ν. The transpose may be written (ΛT)μ ν=Λν μ. I want to apply this to convert the defining relation for a Lorentz transformation η=ΛTηΛ into index form. We have ηρσ=(ΛT)ρ μημνΛν σ The next step to obtain the correct...

Hi, With respect to derivative notation... d/dx(y) //1st derivative of y w.r.t x d/dx (dy/dx) = d^2y/dx^2 //2nd derivative d/x (d^2y/dx^2) = d^3y/dx^3 //3rd derivative If you continue finding derivatives in this way, why do the d's increment in the...

Background info (Not actual question): So I've been gone a week from university and I've missed a lot of content, one particular thing that boggles me is this new method to operate with vector magnitudes and their angles. The operations surprised me with the speed they were done. I did ask a...

Homework Statement can someone help me express mm In negative powers notation. S Thank you Homework EquationsThe Attempt at a Solution

Can someone tell me what this notation is \hat e =\frac{\overrightarrow{u}\cdot \overrightarrow{v}}{|| \overrightarrow{u}\cdot \overrightarrow{v}||} = -\frac{\overrightarrow{v}\cdot \overrightarrow{u}}{|| \overrightarrow{u} \cdot \overrightarrow{v}||} I saw it here...

Homework Statement I am trying to convert following from infix to post fix: (4+8)*(6-5)/((3-2)*(2+2)) I am facing problem at character 20 which is a ‘(‘ i.e. opening bracket. Homework Equations There is no eq but the algorihm is given below: I got following algorithm from internet. 1...

I need help understanding this notation, what does this mean? Squared of 2-norm? 1. Homework Statement Thanks

Hey all! Thanks for reading. I'm currently following along in some reading and had some trouble with re-writing a Hamiltonian in Bogluibov-de Gennes form using Nambu notation (Nambu spinors). Here is the low down: Say we have a Hamiltonian: \frac{1}{2} \sum_{i=1}^{N} c_{i}^{\dagger} D c_{i} +...

Homework Statement find domain f(x)= ## \frac{\sqrt{x^2-x-6}}{x-5} ## Homework EquationsThe Attempt at a Solution [/B] Well, one sees that x ≠5 and then we further investigate the dividend portion where the under-the-root expression ≥ 0 We can graph the parabola, and find the zeroes. Then...

I was just reading a cryptography book and have a question about something the author states I highlighed the statement in yellow and included a pictures. So I was wondering if the function could be written as E(M,K) = C instead of Ek(M)=C since the fact that E is dependent on K. If not why...

The question asks me to determine whether the function is continuous? f(x)=1, x =0,1 f(x)=x+[2x], 0<x<1 what is this [2x]? I cannot find it in the textbook and during lecture we had no information given about this.

Okay so when there is time-translation symmetry because the metric components do not have any time- dependence, ##\partial_x^0## is a Killing vector. I'm just confused what this means explicitly, since a derivative doesn't make sense without acting on anything really? But by 'spotting the...

Hi, I have a long differential equation which I am typing into mathcad. I want to use either dot or dashed notation instead of d/dt to shortern it and make it more readable. Do you know how I can do this so that it actually recognises it as a derivative? I

Let's say I have two vector fields a(x,y,z) and b(x,y,z). Let's say I have a scalar field f equal to a•b. I want to find a clean-looking, simple way to express the directional derivative of this dot product along a, considering only changes in b. Ideally, I would like to be able to express...

We've been learning about tensor products. In particular, we've been looking at index notation for the tensor products of matrices like these: ## \left( \begin{array}{cc} a_{11} & a_{12} \\ a_{21} & a_{22} \end{array} \right)## And ## \left( \begin{array}{cc} b_{11} & b_{12} \\ b_{21} & b_{22}...

Homework Statement Can someone please check my working, as I am new to Einstein notation: Calculate $$\partial^\mu x^2.$$ Homework Equations 3. The Attempt at a Solution [/B] \begin{align*} \partial^\mu x^2 &= \partial^\mu(x_\nu x^\nu) \\ &= x^a\partial^\mu x_a + x_b\partial^\mu x^b \ \...

Homework Statement Hi guys, I am having a issue with the notation of this question. I can workout what to do, but I don’t understand what is $$C^+,C^{++}$$ Could someone please explain. My thought is maybe is 2 carbon atoms bonded together? Homework EquationsThe Attempt at a Solution

I bought a maths book and have discovered it's somewhat above my level. In particular I'm confused about one bit of notation. I understand the "is a member of" operator when it takes a set as argument (e.g. n ∈ ℝ) but not when the book uses it with functions (e.g. n ∈ f) Does n ∈ f mean that...

What is the correct way to write the product rule in Newton notation (with the dots above)? It is the LHS I am abit confused with. Eg. Say you have d/dt(xy) would you just put dots above the x and y?

Hi is there a way or algorithm to find the sigma notation of sums in which the sums do not have an apparent general form?

Hello. I think excited states of Argon atom is described by j,l coupling written as (2s+1)[K]J. However, when I read some papers describing cross section data for Argon atom, data are quoted with strange notation, Paschen notation. I tried to study the Paschen notation and found that its form...

I am almost ashamed to put this question, as it verges on the silly, but it is a real question, and Physics Forums has come to my rescue so often... I am translating a physics article from Russian, and at one place the author puts quantities (such as σ for standard deviation, etc.) with a double...

I'm not used to Einstein notation and I'm struggling a bit with the more complex examples of it. I got the general gist of it and can follow the basic cases but get sometimes a bit lost when there are a lot of indexes and calculus is involved. All primers I've found online for now only give the...

Looking at relativistic transformations and suddenly we have this transformation matrix with an upper and lower index. See below: A bit of googling tells me the upper index means a co-ordinate. However I'm not sure what the lower index is. Overall I have no idea what makes it so special, or...

In one of our lectures we wrote Maxwell's equations as (with ##c=1##) ##\partial_\mu F^{\mu \nu} = 4\pi J^\nu## ##\partial_\mu F_{\nu \rho} + \partial_\nu F_{\rho \mu} + \partial_\rho F_{\mu \nu} = 0## where the E.M. tensor is ## F^{\mu \nu} = \begin{pmatrix} 0 & -B_3 & B_2 & E_1\\ B_3 & 0 &...

There is some confusion regarding notation of the arguments of a probability distribution. For example, MLE is defined as estimating the distrubution that gives the maximum probability of the observations x_i given the distribution parameters, p(x|\theta) . However my instructor stressed that...