What is Indices: Definition and 206 Discussions

If j^\mu = ( j^0 , \vec{j} ), why does \partial_\mu j^\mu = \partial_0 j^0 + \vec{\nabla} \cdot \vec{j} surely when you take a dot product of four vectors you get a subtraction as in a^\mu b_\mu = a^0 b_0 - \vec{a} \cdot \vec{b} Maybe I'm forgetting something

if I have an expression gca * dwab is there any reason for the resultant tensor should be dwcb vs. dwbc?

This is from Linearized Gravity in General Relativity, where h is the perturbation on the background Minkowski metyric. Is the following valid...

Well, this isn't so much for general raising and lowering of indices. It's a specific step within the formation of the Ricci Tensor in the Linearized Gravity problem. I trying to get from 7.5 to 7.6 in Sean Carrol Spacetime and Geometry, page 275. I'm not matching with the 2nd term in...

I'm currently doing a project in my materials class and I wanted to check if these two material indices were right. The objectives are: 1. The material must not fracture 2. The material must be strong (no deformations) Material Index 1 ------------------------ Considering a yield-before-break...

Ok, so I have this Expression, (6x+2 x 42x-4 x 35-x x 2x-6)/(124x+3 x 92x-3) But it needs to be simplifyed, and expressed with positive indices. Now as far as my knowledge takes me, this can't be simplifyed, but then I am probably wrong. If anybody could help to solve, that would be great.

Simplify and express with positive indices, a little help? I am no good at these, can anyone show me how to work these out? (18x3 X 2x-4)/(4x-5 X 6x) 83sqrt(p12 q-8) X 34sqrt(p-10 q9) and (6x+2 X 42x-4 X 35-x X 2x-6)/(124x+3 X 92x-3) ps. The Capital X's are multiplication signs

I have a 100x1 vector A, and want to know the ten indices i for which A(i) are the greatest 10 values in A. I can find the values by: B = sort(A) B(1:10); But I don't know how to find the indices, apart from starting a new if loop which searches the entire matrix (which seems very time...

Homework Statement 2^x+3^x=13, x=2. How do i prove it? The Attempt at a Solution i did this x log 2 + x log 3 = log 13 x(log 2 + log 3)=log 13 x(0.301+0.477)= 1.11 0.778x=1.11 x=1.43

Simplify: x4yz3 / x3y3z My answer was: xy-2z2 However, the correct answer appears to be: xz2 / y2 I know that y-2 is the same as 1/y2 so would my answer still be marked as wrong in an exam?

I'm not sure I understand how: T^{\alpha \mu \lambda}A_{\mu}C_{\lambda}^{\gamma} = D^{\gamma \alpha} "Represents 16 different equations..." My thinking was that \alpha and \gamma each have four possible values \left\{0,...3 \right\} so we have 4 \cdot 4 = 16 different...

Hi, why can I raise and lower indices of a partial derivative with the help of the metric tensor? E.g., wh is the following possible? (\phi is a scalar function) \partial^\mu \phi = g^{\mu\nu}\partial_\nu \phi -- derivator

Let {x1, x2, x3, x4, x5} be distinct real numbers. Prove there are indices a, b with 0< xa-xb<1+xaxb. Seriously I have no idea how to even start... I tried subbing random numbers in... but nope... Can anyone give a hint? Hey wait, the sets do not need to be ordered right? Can I do...

Homework Statement Let the Fibonacci sequence Fn be defined by its recurrence relation (1) Fn=F(n-1)+F(n-2) for n>=3. Show that there is a unique way to extend the definition of Fn to integers n<=0 such that (1) holds for all integers n, and obtain an explicit formula for the terms Fn with...

Suppose i have a plane in a cubic cell that cut across the following intercepts: x=-1, y= -5/12 z=parallel. What is the miller indices of a triangular plane located at the top left corner of this rectangular plane? Can anyone explain how to solve this? answer is not important.

Homework Statement Show by manipulating the dummy indices, that (Z\underline{abc} + Z\underline{cab} + Z\underline{bca})X\overline{a}X\overline{b}X\overline{c} = 3Z\underline{abc}X\overline{a}X\overline{b}X\overline{c} Homework Equations The Attempt at a Solution This question...

Hi Not sure if this is the best place to post this question but.. Why can we expand (\partial_\mu \phi)^2 in this way: (\partial_\mu \phi)^2=(\partial_\mu \phi)(\partial^\mu \phi) I mean [anything]^2 should equal [anything]*[anything] - why have be raised one of the indices above...

In my Physics lab, I'm doing X-Ray diffraction and attempting to determine the crystal structure of some common salts. To do this, I first need to determine the Miller Indices for the crystal structures that I'm considering. I can then match the location of peaks in X-Ray data (we're using...

Hi!I have got problem on Indices ( which i think i 'm not nearing any solution ) Homework Statement Well the sum is a m^n= (a m)n Now it is to be expressed in terms of n Homework Equations none The Attempt at a Solution I tried this way as the bases are same .: m n= m...

My lecturer has written A | \alpha_n> = a_n |\alpha_n> => A = \sum_n a_n | \alpha_n>< \alpha_n | and B | \alpha_k> = b_k |\alpha_k> => B = \sum_k b_k | \alpha_k>< \alpha_k | Where A is a hermitian operator. I understand he's used the properties of the unitary projector operator here, but is...

Homework Statement A penny is located at the bottom of a barrel of water 1m deep. There is a 20cm thick layer of oil on top of the water. To an observer at normal incidence, what is the apparent depth of the penny. n for water is 1.33, for oil it is 1.5 Homework Equations Snell's law...

Hi all. I am a PhD student in a condensed matter group. Consider: I observe superlattice reflections due to ferrimagnetic order that requires one cell parameter to be multiplied by M, the next by N and the third by O . In other words, the magnetic order is described by a magnetic unit...

I'm having some trouble breaking into tensors. What is specifically bewildering me is contravariant vs. covariant indices. Could someone please explain this to me (or link me)? I barely understand what each one means in its own right, let alone the differences between the two.

Hello, there. I'm having a small problem with Miller's indices. 1) Imagine that the plane (2 1 1) is given in the fcc lattice. How can I determine Miller's indices of that plane in the sc and in the bcc? 2) And after that, how can I find the density of lattice's points? 1) So far I took the...

I've always just accepted that x^\frac{1}{2}=\sqrt{x} but I don't understand why. I guess I'm looking for a proof for this, and possibly lead this onto: x^\frac{m}{n}=\sqrt[n]{x^m} Thanks.

This may be a stupid question or have a pretty obvious answer, but I can't seem to find one so I'll just go ahead and post :) I was looking at some empirical data for relationships defining (abstracted) values for ionization and recomination coefficients in gases as a function of electric...

Theoretical physics presents what I think is potentially an interesting bunch of sociology-of-science case studies and examples. There is one guy (a string PhD named Ozzy Zapata) who is blogging specifically about this, has some fascinating comment: http://spinningthesuperweb.blogspot.com/...

1. (a) Remembering the distinction between summation indices and free indices, look at the following equations and state whether they conform to tensor notation, and if not why not: (i) Tmn=Am^nB (ii) Uij^i=Ai^kDk (iii) Vjk^ii=Ajk (iv) Ai^j=Xi^iC^j+Yi^j (b) (i) Write out in...

I am trying to get a hang of miller indices and doing some practice. So here it is : What would be the miller indices of the plane containing the x-axis and equally inclined to y and z axes? (I have uploaded the diagram and highlighted the plane to clarify) Attempts : I first try to...

In curved space, can I raise an index on a tensor that is being differentiated? Ie, is the following true? g^{\mu\lambda}\partial^\nu(F_{\mu\nu})=\partial^\nu(F^\lambda_\nu)

Wilczek's "Lightness" and other indices Wilczek's "Lightness of Being" gives an up-to-date non-string vision of fundamental physical reality and the ongoing effort to understand it. First published in 2008, it is currently the most visible post-string foundations book for general audience. I...

Homework Statement Hi all. I am looking at a potential with two wells, where we denote the wells a and b. Now there are two electrons in this setup, which we label 1 and 2. I have the following innerproduct: \left\langle {\phi _b (x_1 )} \right|\left\langle {\phi _a (x_2 )}...

Let's say that some non-operator (having only numbers as it's components) tensor is antisymmetric: \omega^{\sigma\nu}=-\omega^{\nu\sigma} and \omega_{\sigma\nu}=-\omega_{\nu\sigma}, however, I have read in the Srednicki book that it is incorrect to say that the same tensor with one...

Hello, I don't understand what is the difference between. e.g. the (1,1)-tensor T_{a}^{b} and T^{b}_{a}, i.e. when the lower and upper indices are exactly the same but in another "vertical order", one slightly to the left and the other one slightly to the right. Thanks for your help!

1. Find value of x if: 4x-1 = 1/32 3. I know that both 4 and 1/32 can be expressed as powers of 2 so (22)x-1 = 2-5 Heres what I am not quite sure about Im just assuming that I multiply that -1 by the power inside the brackets but I am not sure if that's right. Anyhow here's what i...

Homework Statement A question asks me to show the Navier-Stokes equation reduces to u_{t} - Vu_{y} = {\nu}u_{yy} which I have done no bother. Then it asks to find an appropriate solution for u(y,t). Homework Equations The Attempt at a Solution I'm seeking a similarity...

From Carroll's textbook: 1. The problem statement Imagine we have a tensor X^{\mu \nu} with components X^{\mu \nu} = \begin{pmatrix} 2 & 0 & 1 & -1\\ -1 & 0 & 3 & 2\\ -1 & 1 & 0 & 0\\ -2 & 1 & 1 & -2 \end{pmatrix} Find the components of: (a) {X^\mu}_\nu; (b) {X_\mu}^\nu.2. The attempt at a...

So I've taken two differential topology/geometry classes both from a mathematics department. I see all over this forum a whole lot of talk about indices being up or down and raising/lowering etc. My professors barely ever mentioned these things though I did notice that when they worked in...

I have a bit of a problem with this question, I will do my best to offer an answer. I think the problem is not with the differentiation but with my indices. :smile: Here is the initial formula. \int (6x + 2 + x^{-\frac{1}{2}}) dx Here is my attempt :blushing: \frac{6x^2}{2} + 2x +...

in my fields course we are using the metric tensor g=diagonal(1,-1,-1,-1), off diagonal(0) i'm looking for an explanation of why the time coordinate has to be orientated oppositely to the spatial coordinates. can anyone give me an explanation of this? i'm also lost with upper and lower...

The Volume and surface area of a sphere is 4/3πr^3 and 4πr^2 respectively. V=4/3πr^3 and S=4πr^2. Write a) S in terms of V and b) V in terms of S Im stuck on this question... I write out similar base units and stuff but it doesn't seem to work, any help? -The answer to part a is S=2^2/3...

A scientist notices that an oil slick floating on water when viewed from above has many different rainbow colors reflecting off the surface. She aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). The index of refraction of water is 1.33. The index of...

i have a question. please tell me the Miller Indices for Crystal Planes of HCP unit cells +packing density of it. thank you

Complex numbers - polar form - does this work (indices) ? hey i haven't studied in class complex numbers yet, but i know some of the basis , and i was wondering if something i saw in complex numbers was true : polar form : let 'a' be the angle and x the length (dont know how to call it...

They confuse me. If someone tells me a plane has the index, say (233), it's very difficult for me to see where it intercepts the crystal axes. What are they good for?

Hi, Apologies if this is in the wrong place but I've no idea what *it* does... I should just mention that I'm currently doing my A-levels (16) and so my maths skills aren't that advanced... The problem: I've found a paper on the Kalman Filter on the internet (source...

Something I have been curious about, but never had the time to think about is, I know that; x^{3/2} = \sqrt{x^{3}} But I have never seen any proof of this. Does anyone have a good resource or can show me the proof here? It would be much appreciated. ~H

I am new to understanding Miller indices (its never been covered in a class that i have taken etc) and there is a notation that i am seeing in the scientific literature that i don't understand. -Its the notation used after the (h,k,l) numbers. here are a few examples (I put in bold print the...

I'm not exactly sure what to do here after I find the direction, can anyone help me out? Thanks: Sketch the \left[ {0\overline 1 1} \right] direction. Which {110} and {111} plane(s) does it lie in?

A parallel beam of light containing two wavelengths, 1 = 400 nm and 2 = 650 nm, enters the silicate flint glass of an equilateral prism with an angle of incidence of 49 degrees. At what angle, relative to the normal, does each beam leave the prism? This seems simple, but previously, I had...