Indices Definition and 193 Threads

  1. R

    Is there a special term for refractive indices when 1 is subtracted?

    I have been doing a bit of studying for my optics course and I have often come across refractive indices or materials being presented as n-1 (which often makes a lot of sense). I was just wondering if there was a special term like for this format or if we still call it just the "refractive...
  2. Nono713

    MHB Snell's Law and complex refractive indices

    OK, I've looked around the net but there just doesn't seem to be a straightforward answer that doesn't require you to be an electromagnetics guru, so I'm hoping someone on here can help me out. I have a light wave incident to a planar interface, coming from a medium with complex refractive...
  3. H

    Color Indices and Absolute and Apparent Bolometric Magnitude

    Homework Statement Given: Spherical blackbody with surface temperature of 30000K radius of 6.0 x 10^9 m located 123pc from earth Homework Equations Find the absolute and apparent bolometric magnitudes The Attempt at a Solution My camera needs batteries so I cannot post my work...
  4. P

    Efficiently Lowering Tensor Indices: Simplified Equations

    Hi have i got this corresct : g_{\mu\nu}g_{\mu\nu}T^{\mu\nu} = T g_{\mu\nu} = T_{\mu\nu} and is: g_{\mu\nu}g_{\mu\nu}u^{\mu} = g_{\mu\nu} u_{\nu} = u_{\mu}
  5. B

    Contracting over indices chain rule

    Homework Statement As part of a problem I am doing I am asked to show uβ∂βuα = aα where u is 4 velocity and a refers to 4 acceleration. The way to do this is not immediately obvious to me, especially since the problem implies there should be a chain rule step involved which I am not seeing. I...
  6. N

    Miller indices of Ni based alloys

    I was wondering if anyone could give me some info on what the miller indices of Inconel 600 and 690 alloys are. I know they are FCC structure, but does that automatically give them the conventional numbers, or is it something else since it is a complex alloy?
  7. D

    Java How Should Initial Values Be Handled When Calculating EMAs in Java?

    Hi All, I'm working on a little side-project (not school related) in Java for analyzing Financial Stocks (I understand the stuff I'm doing can be done online but I'm trying to learn some graphing/plotting in Java). Anyways, my question has to do with calculated EMAs (Exponential Moving...
  8. O

    How to construct gamma matrices with two lower spinor indices for any dimension?

    Generally, Gamma matrices with one lower and one upper indices could be constructed based on the Clifford algebra. \begin{equation} \gamma^{i}\gamma^{j}+\gamma^{j}\gamma^{i}=2h^{ij}, \end{equation} My question is how to generally construct gamma matrices with two lower indices. There...
  9. I

    Linear Programming Involving Indices

    Homework Statement A marketing team is given a budget of 30,000 to advertise a new show. It wants to promote this show using two methods, internet and posters. The executives have decided that the overall budget used on the internet can't be greater than double the budget used on posters...
  10. M

    How Do Indices Function in Tensor Notation?

    I was wondering how the indices of tensors work. I do not understand how the indices of tensors in can be used. For example, \eta _{\mu \nu }, the metric tensor, is like a matrix, and x^{u} is a contravector. How does this extend to notations such as T{_{a}}^{bc} and T{_{ab}}^{c}?
  11. Borek

    LaTeX [LaTeX] isotopes - how to align left indices?

    So, I have this equation: ^{137}_{55}Cs \rightarrow ^{137}_{56}Ba + e^- + \bar{\nu}_e What I don't like about it is that both 55 and 56 are left aligned and there is a gap between numbers and Ba symbol. I guess I could try to hand align them using spaces and negative spaces, but I also...
  12. W

    Upper limit of Miller indices of BCC and FCC crystals?

    does anybody know the upper limit of the bcc and fcc metals like Fe, Cu, Ag? According to the fact that the planes with high (hkl) indices have small interplanar spacing d_hkl, the smallest spacing would be present. what is that? atomic diameter of a specifc metal?
  13. M

    Snell's Law, indices of refraction

    Homework Statement A beam of light in air is incident on a stack of 4 flat transparent materials with indicies of refraction 1.20, 1.40, 1.32, and 1.28. If the angle of incidence for the beam on the first of the four materials is 60*, what angle does the beam make witht the normal when it...
  14. A

    Can You Shift an Array by a User-Inputted Value Using For Loops?

    So I am trying to use for loops to shift the index an array by a user inputted value. The code i have so far is printMessage(); cin >> choice; if(choice == 2){ cout << endl; cout <<"Please enter...
  15. G

    Difference between longitudinal and transverse refractive indices

    hi All, as the title suggests, I a not so clear on the difference between the two. in particular in solids, I have been looking at various approached to calculating the refractive index. But I´m not so clear on why there is two descriptions of we have a homogeneous medium. thnks!
  16. homology

    Raising/Lowering indices and matrix multiplication

    Please read the following carefully. The point of the following is to distinguish between T^{\mu}_{\mbox{ } \nu} and T_{\mbox{ }\mu}^{\nu} which clearly involves a metric tensor. But when you want to go from component manipulation to matrix operations you have to be careful. Components are...
  17. E

    Transpose of a matrix with mixed indices

    Hi! Given a matrix A of elements A_i\;^j, which is the right transpose: A_j\;^i or A^j\;_i ?
  18. S

    Miller Indices (Solid State Physics)

    Homework Statement A simple cubic crystal with lattice parameter 0.5 nm has a plane which intersects atoms at the points (-0.5,-0.5,0), (1,-0.5,0.5) and (1,2.5,-1.5), where the coordinates have units of nm. What are the miller indices of the plane? Having read the relevant chapters of...
  19. N

    AS Mathematics - Core 1 - Indices Problems

    I am struggling with my mathematics indices homework. I think I have some correct answers so far but I'm pretty stumpted on some others. How would I go about solving the following equations. Homework Statement 1) 25 to the \frac{1}{2} - \frac{5 to the -4}{5 to the -5} Homework...
  20. S

    Calculating κ: Find the Value of (√3)^7 + (√3)^5 + (√3)^3 + 42(√3)

    Given that (√3)^7 + (√3)^5 + (√3)^3 + 42(√3) may be expressed as 3^κ, find the value of κ Now I know that (√3)^ 7 is the same as 3^3.5 so I have 3.5, 2.5 and 1.5 but i have no idea how to calculate 42 (√3). Please help :(
  21. sankalpmittal

    A problem on algebric expansion and indices.

    Homework Statement If : p2+q2+4r2 = pq+2qr+2rp Prove that : p=q=2r Homework Equations I am not sure but I tried using this equation : (a+b+c)2 = a2+b2+c2+2(ab+bc+ca) The Attempt at a Solution p2+q2+4r2 = pq+2qr+2rp p2+q2+4r2 -pq-2qr-2rp = 0 Now I can't factor. Its not...
  22. P

    Vector Problem. Free and dummy indices?

    (ABC)ij =Xk Xl AikBklClj where x is the sum of In the above equation which are the dummy indices and which are the free indices? I think i and j are free, and k and l are dummy. But I am not surre!
  23. N

    Calculations with Weyl Spinor Indices in QFT

    Homework Statement The task is to show the invariance of a given Lagrangian (http://www.fysast.uu.se/~leupold/qft-2011/tasks.pdf" ), but my problem is just in one step (which i got from Peskin & Schröder, page 70) which i can not reproduce due to my lack of knowledge regarding spinors. The...
  24. F

    How to loop on vector values and have indices too

    i want to loop on K vector values K = [3 5 7 9 11] and have with me inside the loop the index of the current vector value if i made for K = [3 5 7 9 11] disp(K) end i'll not have the index of K values i mean when K=9 i want to know that I'm in index 4 how to make that??
  25. D

    Fourier transform, range of indices

    hi, could someone explain the following statement, please? Why is the real data only shifted, but the Fourier space data is 'wrapped around'? The only difference should be: exp(k*x*2*i*Pi/N) in reals space vs. exp(-k*x*2*i*Pi/N) in Fourier space. Both have a periodicity of N. So why is there...
  26. V

    Confusion with lower/raising indices

    will the following actions be appropriate g^{\mu\sigma}\frac{dA_{\sigma}}{d\tau}=\frac{dA^{\mu}}{d\tau}Please let me know, I will be glad if you can explain too. thanks
  27. R

    What Angle Must Light Make at the Water-Oil Interface to Prevent Escape?

    A tank of water (nwater = 1.33) is co v e r e d w i t h a l a y e r o f oi l (noil = 1.48), a b o v e w h i c h is a i r ( n ~ r - - 1.00). W h a t a n g l e m u s t a b e a m o f l i g h t , o r i g i n a t i n g i n t h e t a n k , m a k e a...
  28. J

    Definition of observability indices?

    If someone could please provide me with a simple explanation for observability indices I would be most grateful! According to wikipedia; "The Observability index (v) of a linear time-invariant discrete system is the smallest natural number for which is satisfied that rank(Ov) = rank(Ov + 1)"...
  29. A

    Solving Indices Problem in QFT

    Hi, I always seem to have a problem with my indices... \Lambda^{\mu}_{\;\;\nu}\Lambda_{\bar{\nu}}^{\;\;\mu}= \frac{\partial x'^{\nu}}{\partial x^{\mu}} \frac{\partial x_{\bar{\nu}}'}{\partial x_{\mu}} Now, the first term I'm relatively sure is right (first lambad corresponds to first of the...
  30. A

    How Are Tensor Indices Ordered in Calculations?

    I would welcome advice on the practical issues of manipulating tensor indices, in particular how to determine the order of indices during calculations. Some of the following questions are probably simplistic but I have been unable so far to find a consistent answer. 1) Some texts use a unique...
  31. S

    Plane Indices: An Interesting Debate

    Hi Guys, What are the milled indices of plane (see attached figure). Its very interesting...and I am receiving every-time different answer from others. Have a look. Shriphy
  32. V

    What is going on with the indices

    If: \delta x^\mu = a^\mu +w^{\mu}_{\nu}x^\nu How would we go about working out \delta_1 \delta_2 x^\mu This is apparently equal to: (w^{\mu}_{1}_\nu a^{\nu}_{2} + w^{\mu}_{1}_\lambda w^{\lambda}_{2}_\nu) x^\nu but I can't understand what is going on with the indices - can someone help me...
  33. C

    Solving Confusing Indices in Operator Calculus

    Sorry if this is a stupid question but I really want to understand this. If we have an operator that's defined in the following way: D_\mu \phi^a = \partial_\mu \phi^a - iA^{r}_{\mu}{(T_r)^a}_b\phi^b How would we go about working out: D_\mu D_\nu \phi^a What's confusing me is that the...
  34. M

    MATLAB Simple MATLAB- how to find indices of max element in matrix?

    Hi, Say I have a 10x10 matrix, is there a simple code to finding the indices of the maximum value? I'm trying to use max() but there doesn't appear to be any option of actually returning the index, rather than the value. I don't need the value, just the position. Thanks, Mike
  35. Y

    How the x-ray diffractometer caculate the lattice constant or miller indices?

    Bragg's law n.lambda=2d sin theta. d=1/{h^2/a^2+k^2/b^2+l^2/c^2} for orthorombic structure. thus d=n.lambda/2 sin theta=1/{h^2/a^2+k^2/b^2+l^2/c^2} lambda and theta are given. Look, there are two types/sets of unknowns in the d formula, they are miller indices h, k, l and lattice constant...
  36. M

    Miller Indices of Simple Cubic Lattice

    I'm trying to get my head around indexing x-ray diffraction patterns and this thought experiment stumps me. Let's say I have a crystal with a simple cubic lattice structure: http://ecee.colorado.edu/~bart/book/sc.gif I align a narrow x-ray beam incident on the crystal so that the x-ray...
  37. U

    In the second quantization spin operator, what are Pauli spin vector indices?

    If you look up the second quantization spin operator, you'll notice that there are two indices on the pauli vector for two possible spins. The operator sums over these two indices. Since the pauli vector is an unchanging quantity what do these indices physically correspond to?
  38. R

    Miller indices in Debye-Scherrer method

    Homework Statement Explain how we can determine Miller indices corresponding to the diffraction lines? Can someone explain it for me please? Homework Equations The Attempt at a Solution
  39. N

    Interpretation of tensor indices

    Hi I am trying to figure out the physical interpretation of tensor indices. E.g., if we have an anisotropic material, then the tensor element of the susceptibility xx,y gives the response in the x-direction of an electric field in the y-direction. Lets not go up one dimension and look at...
  40. J

    Pauli matrices with two spacetime indices

    "Pauli matrices with two spacetime indices" Hi all. This is my first post so forgive me if my latex doesn't show up correctly. I am familiar with defining a zeroth Pauli matrix as the 2x2 identity matrix to construct a four-vector of 2x2 matrices, $\sigma^\mu$. I'm trying to read a paper...
  41. Saladsamurai

    Power Series Change of Indices: I broke math again

    Homework Statement I have an infinite series that looks like this: \sum_0^\infty n(n-1)d_nx^{n-1} + \sum_0^\infty n(n-1)d_nx^n + \sum_0^\infty d_nx^nI wish to combine all three sums so that they must all have same powers of x and start at same index. The second and third summations are fine...
  42. R

    Prime Indices & the Divisors of (p'_n - 1): A Lattice-Related Question

    Prime Indices & the Divisors of p'_n - 1 such that Divisors & Indices are equivalent for... p'_n an element of {N} | d'(n) < or = to 2 This set of integers is equivalent to 1 Union the Prime Numbers aka "Primes at the beginning of the 20th Century" where... d'_n denotes the number of divisors...
  43. L

    Understanding the Continuity Equation in Special Relativity

    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
  44. C

    Is there any reason for tensor indices being ordered one way or the other?

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

    Help With Raising and Lowering Indices

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

    Help With Raising and Lowering Indices

    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...
  47. J

    Simplify and express with positive indices

    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.
  48. J

    Simplify and express with positive indices, a little help?

    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
  49. M

    Retrieving Indices of a vector whose elements fulfil a criteria

    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...
  50. C

    But we can't show that x = 2 is the only solution.

    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
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