Representation Definition and 722 Threads

Homework Statement You always see slope represented as \frac{\delta y}{\delta x}. Is there any particular reason for why the change in "y" is in the numerator and the change in "x" in the denominator? Why couldn't we represent it as delta x over delta y? Homework Equations \frac{\delta...

I would like to have a setup/software to geometrically simulate or represent the given molecule. For example I will input ; 2 hydrogen + 1 oxygen and it will output h2o and draw it's molecular shape. Also it would be much better if the software could give all the possible combinations of the...

1. Homework Statement [/b] Show that the matrix representation of the dihedral group D4 by M is irreducible. You are given that all of the elements of a matrix group M can be generated from the following two elements, A= |0 -1| |1 0| B= |1 0| |0 -1| in the sense that all...

Homework Statement I just now came to the realization that I don't know the standard for representing units. When do I include "." after the abbreviation and when do I not? Thanks. For example mi. or mi m or m. yr. or yr What's the rule? I'm sure there's got to be some general...

Just started my way ploughing through Weinberg's book, for which my progress can be measured in lines since I got so many confusions. I suppose there'll be more confusions awaiting me, so I wish all my confusions or questions from his book will make a series, and I'll label them as...

Kindly ignore if some +- signs are placed wrongly in the equations. Thank you. Rotation in three dimensions can be represented using pauli matrices \sigma^{i}, by writing coordinates as X= x_{i}\sigma^{i}, and applying the transform X'= AXA^{-1}. Here A= I + n_{i}\sigma^{i}d\theta/2. The pauli...

Does someone know a textbook that treats QM without relying on representations much? I mean like saying "lets show that this commutator (momentum and position etc.) is reasonable and then derive everything from that without ever talking about representation much". Moreover is it possible to...

I need a free description with illustrations on 4D knots theory, especially the 4D generalization of Reidermeister moves and the movie represantation. Where can I find a freely available paper?

Hello, this might be a basic question. In feynman diagram's we represent the positron as traveling backwards in time. Is that correct ? How do we interpret this ?

Homework Statement Find a power series representation for the function and determine the radius of convergence.Homework Equations f(x)=x^{2}tan^{-1}(x^{3})The Attempt at a Solution I don't have any idea on how to even start this. First I differentiated \frac{d}{dx} arctan(x)=\frac{1}{x^2+1}...

I have 3 basis vectors: e_1 = sin^2(x), e_2 = cos^2(x), e_3 = sin(x)cos(x) I am told that the combination rule is just normal addition, and that the differential operator is defined by Dp(x) = p'(x). My task is to show that D =...

T is a linear operator from the space of 2 by 2 matrices over the complex plane to the complex plane, that is T: mat(2x2,C)\rightarrowC, given by T[a b; c d] = a + d T operates on a 2 by 2 matrix with elements a, b, c, d, in case that isn't entirely clear. So T gives the trace of the...

There the well known theorem that every open set (I'm talking about R here with standard topology) is the union of disjoint open intervals. Now, looking at the geometry, it seems that between any two adjacent open intervals which are in the union constituting our open set there is a closed...

Hey all Homework Statement Here i want to translate them and show the hex representation of these instructions: 1)add $t0, $t0, $zero 2)lw $t2, 16($s3) Homework Equations The Attempt at a Solution eg. 2) lw | $s3 | $t2 | 16 I-TYPE then translate the assembly code: 35 | 19 | 10 | 16 The...

Homework Statement Show that \int d\theta e^{\theta(\xi-\eta)}=\delta(\xi-\eta), where all of the above variable are Grassmann numbers. All this is in the holomorphic representation, where for some generic function: f(\theta)=f_0 + f_1\theta Homework Equations How do I arrive at that...

Find a power series representation for the function and determine the interval of convergence. f(x)=\frac{1+x}{1-x} This is one of the few problems in this section that I am getting stuck on. I know that I can relate it to the form of; \frac{1}{1-(x)} ...but after that I don't know what...

Homework Statement Find a power series representation for the function and determine the radius of convergence: f(x)=ln(5-x)Homework Equations Manipulate into the form 1/(1-x).The Attempt at a Solution I know how to do this with other functions, say, x/(9+x2)... It would convert to x/9 *...

Homework Statement In order to construct a character table (or to solve problems that directly ask for irreducible representations) I have to be able to decompose a representation into irreducible representations. However I don't know how to do this in general. Homework Equations I...

Homework Statement In order to construct a character table I need the character of the standard representation. The only problem is I don't know how to find the standard representation of a given group. Homework Equations The groupprops wiki tells me: "Take a representation of degree n...

http://awesome.good.is/transparency/web/1104/congress/transparency.png The biggest graph (with the dots) is just for republicans vs. democrats vs. other. But check out the smaller graphs comparing what would actually reflect the american people (on the right) and what is actually there in...

Homework Statement I need to calculate the probability distribution of 1s and 2p state of hydrogen atom in momentum and in coordinate representations. I have calculated the wave function in coordinate representation, and the dilemma is, do I simply do the Fourier transform for given wave...

Hi, I'm new in this forum. I have a problem i can't solve and searching on Google i couldn't find anything. It says: If D(g) is a representation of a finite group of order n , show that K = \sum^{i=1}_{n} D^{\dagger} (g_i) D(g_i) has the properties: b) All eigenvalues of K are...

Below is the Wikipedia URL shows the shape of EM wave. http://upload.wikimedia.org/wikipedia/commons/3/35/Onde_electromagnetique.svg" Electromagnetic laws say that' "changing magnetic field produce electric field and changing electric field produce magnetic field" In the...

Homework Statement Find the Fourier integral representation of the given function. f(x)= \left\{\begin{array}{ll} 1-\cos(x) & \mbox{ if } -\frac{\pi}{2} < x < \frac{\pi}{2} \\ 0 & \mbox{ otherwise} \end{array}\right. On a side note...how does one properly enter the above using...

Homework Statement Compare the function f(z) = (pi/sin(pi*z))^2 to the summation of g(z) = 1/(z-n)^2 for n ranging from negative infinity to infinity. Show that their difference is 1) pole-free, i.e. analytic 2) of period 1 3) bounded in the strip 0 < x < 1 Conclude that they are...

Homework Statement find parametric representation for the part of the plane z=x+3 inside the cylinder x2+y2=1 The Attempt at a Solution intuitively... the cylinder is vertical with the z axis at its centre. and the plane is the whole surface inside the cylinder where y=0... visually...

Homework Statement Find the power series representation for s(x) and s`(x) integral sin (pi t^2)\2 and which of them is valid ? Homework Equations The Attempt at a Solution I tried to solve this question , but i am not sure s`(x) = sin (pi t^2)\2...

Very simple question, but I can't find the answer. Taking an su(n) Lie algebra with hermitean generators we have [T^a, T^b] = if^{abc}T^c One immediately finds that the new generators \tilde{T}^a = (-T^a)^\ast define the same algebra, i.e. fulfil the same commutation relations...

Homework Statement Let L(x) a linear operator defined by setting the diagonal elements of x to zero. What will be the representation of this operator to the following basis set? x E X. X denote the set of all real symmetric 3x3 matrices. Homework Equations L*y=x L=x*inv(y)...

Homework Statement Find a power series representation for the function f(t) = \ln((1+2t)/(1-2t)) Homework Equations f(t) = \ln((1+2t)/(1-2t)) The Attempt at a Solution \ln(1+2t)-\ln(1-2t) take derivative of f(t) expanded \frac{2}{1+2t}+\frac{2}{1-2t} 2 \int \frac...

Homework Statement Determine the value of f(-1) when Homework Equations f(x) = (x/2^2) + ((2x^3)/2^4)+((3x^5)/2^6)+... . (Hint: differentiate the power series representation of ((x^2)-2^2)^(-1).) The Attempt at a Solution I was not very sure were to begin on this one. So I...

Lie algebra \mathfrak{sl}(2,\mathbb{C}) consists of all 2x2 complex traceless matricies. The space of these matricies is 6-dimensional vector space over real numbers field but is 3-dimensional space over complex numbers field. Number of different representations of this algebra depend on how...

Hello All, I'm trying to understand how the (j,j') representation of the Lorentz group. Following Ryder, I can see why we define A=J+iK and B=J-iK, which each form an SU(2) group. So it's clear to me what the rep of these generators is when acting on a state (j,j'): Rep(A)\otimes1+1\otimes...

I am confused with this part of "Introduction to Electrodynamics" 3rd edition by Dave Griffiths. On page 367, the traveling wave is represented by: f(z,t)\;=\; A cos[k(z-vt) \;+\; \delta] [SIZE="5"] 9.7 Where v is velocity and kv=\omega. This give: f(z,t)\;=\; A cos[kz...

Homework Statement I've been looking at Paul Langacker's "Grand unified theories and proton decay" for a course on GUTs. I'm stuck with the 16 irrep of SO(10), particularly I don't understand how to prove the statement that the 16 decomposes as 5* + 10 + 1. I can see why it's useful physics...

Hi, I am currently studying Lie Algebra in Particle Physics' by Howard Georgi. I am finding the notes on Weights and Roots quite confusing. Can anyone suggest another book which explains this bit in a better fashion?

I have a general question about extracting information from measurement of a qubit. Theoretically a qubit in a superposition state contains an infinite amount of information, but when measured collapses to a definite state and result. My question is this: Is there a way to obtain a value from...

Is it true that there are only two inequivalent two-dimensional representation of SL(2,C) group and they are responsible for Lorentz transformation of left and right Weyl spinor.

Homework Statement Given s : \mathbb{N} \to \mathcal{P}(\mathbb{N}) s(n) = \{i | \exists (b_0,\ldots,b_k) \in \{0,1\}^{k+1} [n = \sum_j b_j2^j \,\wedge\, b_i = 1]\} show that s is a bijection between N and the finite subsets of N. In other words, if you express n as the sum of powers...

Hopefully people are still prowling the forums this close to christmas :) I want to show that sin(ax)/x is a representation of a delta function in the limit a->infinty i.e 1) It equals 0 unless x=0 2) integrated from plus minus infinity it equals 1 and 3) multiplying by an arbitrary...

[b]1. Homework Statement : Find the power series for the function f(x)=5/(7-x), centered at c=-2. [b]2. Homework Equations : a/(1-r) [b]3. The Attempt at a Solution : I know that I need to divide by seven to get (5/7)/(1-(x/7)) and then rewrite in the form the sum of (a)(r)^n. I tried adding 2...

My question relates to a specific example, namely the square root of two. If one forms a right isosceles triangle with the hypotenuse equal to 2 (be it metres, centimetres or whatever) then the other two sides must equal the square root of 2. But the square root of 2 is an irrational number. If...

Homework Statement Find the Laurent series representation for f(z)=(z-1)/(z-2) at z=i. Homework Equations NA The Attempt at a Solution I have taken multiple derivatives but I keep getting stuck at what to do after I find my representation of my nth derrivative. PLEASE HELP

I've been asked to express the inverse hyperbolic secant function arcsech in terms of the natural logarithm and am unsure as to where to begin in solving such a problem? could someone please point me in the right direction?

I've just read the statement "The Lorentz transformations have a representation on the fields" Can anyone explain the meaning of the word representation? I can't seem to get a satisfactory explanation anywhere and the notes don't go into much more detail on it.

Power Series Representation of a Function when "r" is a polynomial Homework Statement Find a power series representation for the function and determine the radius of convergence. f(x)=\stackrel{(1+x)}{(1-x)^{2}} Homework Equations a series converges when |x|<1...

Hi This is actually a question regarding some formalism of QM, but I guess this is the place to ask it. Say we are looking at some kinetic energy operator T = T(r, ∇r), which has the form T = \sum\limits_{i,j} {T_{i,j} \left| \psi_i \right\rangle \left\langle \psi_j \right|} in...

Homework Statement Hi guys As we have discussed earlier, we can represent some operator in an arbitrary basis by the use of the 1-operator: T = \hat{1} T \hat{1} = \sum\limits_{\sigma_a,\sigma_b } {\left| {\psi _{\sigma_a} \left( {r_i } \right)} \right\rangle...

Hi all I am struggling with going between various representations of vibrations in paticular the complex form. I am using Rao as my text btw so for a free vibration and making it simple no damping the euqation of motion is mx^{..} + kx = 0 with the general solution being x...

Homework Statement (note; all column vectors will be represented as transposed row vectors, and matrices will be look like that on a Ti-83 or similar) L: R^3 -> R^2 is given by, L([x1, x2, x3]) = [2x1 + x2 - x3 x1 + 3x2 +2x3]* *Matrix Relevant...