Representation Definition and 722 Threads

Homework Statement The function f(x)=10xarctan(5x) is represented as a power series http://img464.imageshack.us/img464/4131/formub5.jpg Find the first few(5) coefficients in the power series. Homework Equations I already know that the representation of arctanx is summation from...

more on the complexification of a vector space. if we complexify some space V, then how does the matrix representation of some linear T on V relate to the matrix representation of T on Vc on the standard ordered basis for V?

Show the matrix representation of S_z using the eigenkets of S_y as base vectors. I'm not quite sure on the entire process but here's what i think: We get the transformation matrix though: U = \sum_k |b^{(k)} \rangle \langle a^{(k)} | where |b> is the eigenket for S_y and <a| is...

Homework Statement Give a parametric representation of the plane x + y + z = 5. Homework Equations I am really not sure, I've been over the chapters we've covered for a little over an hour now, and the only mention i can find of a parametric representation of a plane is in passing...

let X be an operator, we can write X as a matrix where: X = \sum_{a''} \sum_{a'} |a''><a''|X|a'><a'| where <a''|X|a'> a'' are the rows and a' are the columns. I was wondering what happened to the |a''> <a'|? It seems like they are disregarded when transforming to matrix notation. I...

I am going to ask some general questions about representation theory which may sound stupid as I don't know anything about it. How old or new is this theory? How did it come out? What is the general consensus of ths difficulty of the subject? Are there many open problems in this theory? Is...

Hey guys, I was just wondering if you have a good references to the use of Young diagrams/Tableuxs specifically to deduce the representation theory of various Lie groups *other than SU(N)* I know how it works for SU(N) and those groups that can be split into tensor copies theoreof, but I have...

Why has the adjoint representation a higher dimension than the basis matrices it acts on? for example here Why is e_1 two dim and ad(e_1) four dim? Isn't ad(X) Y a simple matrix multiplication here? But then multiplying 4x4 with 2x2 matrices, what does it mean? thanks

Hi, Can someone explain to me why do we actually need the Interaction/Intermediate representation? In my past, each course in QM touched it only for a few minutes and then it got... forgotten. Can someone please give me an example as to how (and when) it is used (and a good reason why)...

Is it possible to derive the Shrodinger's equation i\hbar\partial_t \Psi(t,p) = \frac{|p|^2}{2m}\Psi(t,p) in momentum representation directly from a path integral? If I first fix two points x_1 and x_2 in spatial space, solve the action for a particle to propagate between these...

Homework Statement Using the complex representation of Fourier series, find the Fourier coefficients of the periodic function shown below. Hence, sketch the magnitude and phase spectra for the first five terms of the series, indicating clearly the spectral lines and their magnitudes...

what is the sufficient condition for the kernel of an adjoint representation to be the center of the Lie group? Does the Lie group have to be non-compact and connected, etc?

I'm trying to do the question attached. I got the first three answers correct knowing that the nth derivative of a function evaluated at 0 divided by n! = c_n. However, I did the same for the others and the answer is incorrect. I know that I need the power series representation of that function...

Homework Statement Start with the power series representation 1/(1-x) = sum from n=0 to inf. of x^n for abs(x) < 1 to find a power series representation for f(x) and determine the radius of convergence. f(x)=ln(5+x^2) Homework Equations The Attempt at a Solution Okay, so I...

Question on representation theory. What is the principal representation? I would like a good clear definition. I can't find it in my book (bad index) nor can I find it on the web.

Hi o:) I wasn't able to insert equations here, so here's the link where my problem is described: http://www.advancedphysics.org/forum/showthread.php?t=7696

Homework Statement Find a power series representation for the function f(x) = x / (4+x) and determine the interval of convergence. I have no idea how to begin this problem. My only guess would be trying to divide something out in order to simplify to something that I'm able to...

Hello all, Can anybody help me solve the following exercises from the book: Representation Theory, A first course by William Fulton and Joe Harris,1991 page 138, exercise 10.3 page 140, exercise 10.7 page 141, exercise 10.9 Thanks in Advance,

Homework Statement "A sinusoidal wave is propagating along a stretched stringas a function of time is graphed in the figure (attached) for particles at x = 0 and x =0.0900m. a) what is the period of the wave ( my ans = 0.04 sec b) what is the amplitude of the wave ( my ans = 4mm)...

We have \epsilon(i f, r) = \epsilon_2(i f) when H + h_2(x) \leq z < + \infty \epsilon(i f, r) = 0 when h_1(x) < z < H + h_2(x) \epsilon(i f, r) = \epsilon_1(i f) when - \infty < z \leq h_1(x) show the corresponding Fourier transform is \frac{i}{q_z} \int d^2x e^{iq_\bot \cdot...

I want to find the Fourier coefficients for the following signal: \cos(2 \pi t)^2 Can I simply use the identity?: \frac{1}{2} + \frac{\cos(2 \pi t)}{2} And then use the complex definition: \frac{1}{2} + \frac{1}{4} (\exp{j2 \pi t} + \exp{-j2 \pi t}) From the synthesis equation I can...

Homework Statement Find the matrices which represent the following ladder operators a[SIZE="3"]+,a_, and a[SIZE="3"]+a- All of these operators are supposed to operate on Hilbert space, and be represented by m*n matrices. Homework Equations a[SIZE="3"]+=1/square root(2hmw)*(-ip+mwx)...

Homework Statement Consider the linear map A : R3 ----> R3 given by A(x1, x2, x3) = (x1 − x2,−x1 + x2, x3). (a) Find the adjoint map A^*. (b) Obtain the matrix representations of A and A* with respect to the canonical basis f_1 = [1, 2, 1], f_2 = [1, 3, 2], f_3 = [0, 1, 2]...

Hi everyone, Can anyone explain the following to me? Given a basis beta for an n-dimensional vector space V over the field F, "the standard representation of V with respect to beta is the function phi_beta(x)=[x]_beta for each x in V." This is from my textbook. It then proceeds to give...

I'm doing self study out of Apostol's Calculus vol. I and I got stuck trying to prove what the author writes is easy to verify, but I can't get my head around it. Basically, this is the problem statement from page 31, last paragraph: Given a positive real number x, let a[SIZE="1"]0 denote the...

Homework Statement 1. Obtain an expression for operator of coordinate in momentum representation. To this end begin with definition of the average coordinate x = ∫ψ*(x)xψ(x)dx express the wave functions as wave packets in terms of plane waves, and rewrite the expression for average...

unique vector representation?? Homework Statement So, here I am again with another... The problem gives me a basis {(1,1,1,1),(0,1,1,1),(0,0,1,1),(0,0,0,1)} in F^4. I am supposed to find the unique representation of an arbitrary vector (a1,a2,a3,a4) as a linear combination of the vectors...

I've given the linear transformation L: \mathbb{R}^4 \rightarrow \mathbb{R}^3 , where L(\mathbf x) = A\mathbf x and A = \left[ \begin{array}{cccc} 1&1&-4&-1 \\ -2&3&1&0 \\ 0&1&-2&2 \end{array} \right] The first question of the problem is that, by using the standard basis E for...

Does anyone have any ideas on how to even start this problem? I am supposed to find a general solution in rational numbers for (aside from the trivial ones): x^3+y^3=u^3+v^3 Actually, I'm given the answer (which is really messy) and am supposed to show how to derive it. The book gives the...

Homework Statement find a power series representation for the function and determine the radius of convergence. f(t)= ln(2-t) Homework Equations The Attempt at a Solution i first took the derivative of ln(2-t) which is 1/(t-2) then i tried to write the integral 1/(t-2)...

Hey Everyone, I cannot seem to find an way in Matlab to convert a number which has a real and imaginary part in cartesian form into polar form and then express the polar representation on the output. Ex. Convert z=0.1602932442+0.8277219859*j Into 0.8431<79.04 deg (without using...

Hello all, I have attached a matrix. I am trying to work out this matrix will transform a set of co-ordinates (x_1, y_1, z_1) to a new set of co-ordinates (x_2, y_2, z_2) Can anyone give me any hints on how to tackle this problem?

How do i show the floating point reprensetation of a number like say ... 100! or 1000! in maple?? i am relatively new to maple so i am not familiar with many of the commands

What's the relationship between an certain represetation and the independent variable under this represetation? for details: 1 Must the independent variable of X-represetation be X,and P-represetation must be p?if so ,What's the represetation which basic fuctions are P-latent fuctions...

The first derivative represents the slope of a tangent at a point on the function's curve. The second derivative represents the concavity of the function's curve. However I am unable to figure out what the other derivatives of a function represent either physically or geometrically. Pleae help.

I'm trying to represent graphically the following function: v(t)=3 + 1.414cos(w0t) - 1.414sin(w0t) + 2cos(2w0t + 5pi/2) The problem is that I'm not sure how I represent the sine and cosine both in the same graph...I know that 3 is the continuous component and the w0t equals the "x"...

Hey guys! A question: My QFT Lagrangian, fournishes through Noether's thm plus relativistic invariance a supposedly unitary and a supposed representation of the Lorentz group. These are the operators meant to act on my Hilbert space of possible states. What guarantees that this actually...

I was wondering if anyone knew where I might find, or formulate, the infinite product representation of the entire function f(z) = e^(z). Wikipedia says, and I qoute, "One important result concerning infinite products is that every entire function f(z) (i.e., every function that is...

Hello, From Jean Zinn-Justin: "The conducting plates impose to the electric field to be perpendicular to the plates. It is easy to verify that this condition is satisfied if the vector field A_\mu itself vanishes on the plates. Calling L the distance between the plates, z=0 and z=L the...

I've seen the Fourier representation of the Coulomb potential is -\frac {Ze} {|\mathbf{x}|} = -Ze 4\pi \int \frac {d^3q} {(2\pi)^3} \frac {1} { |\mathbf{q}|^2} e^{i\mathbf{q}\cdot\mathbf{x}} Will anyone show me how to prove it? (yes, it's the Coulomb potential around an atomic nucleus.)...

If I have a faithful nondegenerate representation of a C*-algebra, A: \pi\,:\,A \rightarrow B(\mathcal{H}) where B(\mathcal{H}) is the set of all bounded linear operators on a Hilbert space. And just suppose that a\geq 0 \in A. How is the fact that a is positive got anything to do with...

I've been starting to study some things about representation theory. I've come to the point where they introduced the dual of a representation. Suppose that \rho is a representation on a vector space V. They then define the dual representation \rho^* as: \rho^*(g) = \rho(g^{-1})^t: V^*...

my post i really about discussing the difference that a mathematical representation does to physics. for example, let's take for example a system which can be be represented by quaternions and by complex numbers. if we can represent a physical theory by quaternions which aren't commutative...

Is there a general good way to represent sets as sequences, without wasting data or conveying extra data? One way is a membership list like 11010100111010 but this only works if the possible number of elements is small. I am thinking, data _other_ than ordering, directly about the set objects...

ok, i wasn't sure if i ought put this in math or phys, we're going over it my phys class, but its just math... whatever.. So i had to find the Fourier series representation of x^2 in the intervals (-pi, pi) and (0, 2pi). i haven't even started the (0, 2pi) one, cause i can't get the first...

I'm currently taking my first physics class, and on the very first day, my teacher began discussing vectors as if everyone knew what Unit Vectors were. I've managed to understand most of his lecture thus far, but I still don't understand- How do you convert from Unit vectors (denoted by i...

I have two basic questions about the full propagator (2-point function) in QFT. Am I correct that for a scalar field, it is \frac{iZ}{p^{2}-m^{2}+i \epsilon} + \int_{m^{2}}^{\infty} dX \frac{\rho[X]}{p^{2}-X+i \epsilon} ? (1) Is this form of the propagator a feature of _quantum_ field theory...

may i know how to solve this ques:find the power series representation for arctan (x) i know that arctan (x) = integ 1/(1 + x^2) but then from here i don't know how to continue. pls help...

Has it been done...? If so, any textbook on it...? The concept of Rigged Hilbert Spaces is essential to Quantum Mechanics. Symmetries are implemented in physics by doing representation theory of some symmetry groups, almost all of them being Lie groups: Galilei group, Poincaré group...

Question: Vector field and (n-1)-form representation of current density Electric current density can be represented by both a vector field and by a 2-form. Integrating them on a given surface must lead the same result. My question is, what is the relation between this vector field and the...