Representation Definition and 722 Threads

base representation please help~ It is known that if asks+as-1ks-1+...+a0 is a representation of n to the base k, then 0<n<=ks+1-1. Now suppose n=asks+as-1ks-1+...+a0 and m=btkt+bt-1kt-1+...+b0 with as,bt not equal to 0, are two different representations of n and m to base k, respectively...

1. could anyone give sort of a qualititative explanation of how symmetry and irreducible representation are related in the context of molecular spectroscopy? like why is it so useful to count how many symmetries a molecule has and what does it have to do with irreducible represenations and...

okay so i was reading a book on representations and found this discussion and was confused: http://books.google.com/books?id=Hm-aKMkKXzEC&lpg=PP1&dq=group%20theory%20and%20physics&pg=PA53#v=onepage&q=&f=false it starts at the bottom of pg 53 and ends at the top of pg 54 so I understood the...

Claim: \nabla \cdot \frac{\hat{e}_r}{r^2}=4\pi\delta^3(\vec{x}) Anyone know of a proof of this? (or a reference which covers it?) We need to show that \frac{1}{4\pi}\int_0^R{(\nabla \cdot \frac{\hat{e}_r}{r^2})f(r)dr=f(0). The claimed identity can be seen in the solution for...

I am unable to grasp how to generalise the concept of matrix representation for a group say like D3 or D4.I know how to manipulate the 2x2 matrix,but how do I obtain a group in say a 3x3 matrix to show rotation and reflection?

I'm having trouble grasping what an irreducible representation is. Can someone explain what this is through an example using SU(2) and/or SO(3) w/o invoking the use of characteristic? Like I'm reading a bunch of stuff but I'm not catching the significance of any of it. ...Imagine you were...

We all know that \frac{1}{2\pi}\int{e^{ik(x-x')}dk=\delta(x-x'). i am working a problem which appears to depend on the statement \int e^{z^*(z-w)}dz^*\propto\delta(z-w) Does anyone know if this is valid? \delta(z-w) is defined in the usual way so that...

I heard that angular momentum operators and their eigenvectors are realted to SO(3) or SU(2) group. Does anyone know a good textbook which explain the connection between how group theory and quantum mechanics (especially angualr momentum). I'm interested rather in books which emphasizes...

[b]1. Find a power series for F(x)= 3/4x^3-5, where c=1 [b]2. power series = 1/a-r [b]3. What I did was take a derivative to get a similar function that was easier to solve. I used 1/x^3-1. Then I found a series for that function. Which I got \sum(x^3)^n. Then I added back from my...

My current understanding of the Riesz representation theorem is that it is useful since it tells you what all bounded linear functionals on Lp look like. They look like the integral of fg where g is some function in Lq. So, I was trying to think of an example of a bounded linear functional on an...

can you check my work? "power series representation" is ok I figure it out.

I'm sure my question is very simple to most of u guys. But I have the following confusion. Let's say we have an AC voltage source in a circuit. In rectangular form it's phasor form is v= -4 - 16 j . I want to write this phasor in polar form. Well, The phasor is in 3rd quadrant of complex...

Homework Statement Find a power series representation for f(x) using termwise integration, where f(x) = \int_{0}^{x} sin(t^3) dt . Homework Equations The Attempt at a Solution I've never done this before, but apparently, if I have a power series representation for sin(t^3), I...

I'm trying to calculate the pauli-lubanski pseudo vector for different representations of the poincare group. The first rep is the infinite dimensional "angular momentum" rep where the generators of the lorentz part take the form : M_ab = x_a*d_b - x_b*d_a (for 3 rotations) M_ab =...

In coordinate representation in QM probality density is: \rho(\vec{r})=\psi^*(\vec{r})\psi(\vec{r}) in RSQ representation operator of density of particles is \hat{n}(\vec{r})=\hat{\psi}^{\dagger}(\vec{r})\hat{\psi}(\vec{r}) Is this some relation between this operator and density...

hi, I have a quickon vector spaces. Say for example we have X = a1U1 + a2U2 ...anUn this can be written as X = sum of ( i=0 to n) ai Ui now how can I get and expression of ai in therms of X and Ui. do we use inner product to do this...ans someone please explain how to go...

Hi, I'm currently reading a book on particle physics, which tells me this about SU(3): "...The generators may be taken to be any 3x3-1=8 linearly independent traceless matrices. Since it possible to have only two of these traceless matrices diagonal, this is the maximum number of commuting...

Homework Statement I want to find a matrix representation of the grassman algebra {1,x,x*,x*x} (and linear combinations with complex coefficients) defined by [x,x]+=[x,x*]+=[x*,x*]+=0 I really don't know how to make matrix representations of an algebra. Is any set of 4 matrices that obey the...

Homework Statement Express the surface x = 2cos(theta)sin(phi) y=3sin(theta)sin(phi) z=2cos(phi) as a level surface f(x,y,z) = 144, f(x,y,z) = ? Homework Equations The Attempt at a Solution I figured they wanted the equation f(x,y,z) in x^2+y^2+z^2=144 so I though that by...

Can a generic, not necessarily harmonic, signal of time be represented as a complex signal with a real and imaginary part? Usually the complex rappresentation is used for time harmonic signals and linear systems. The "real" time signal is transformed into a complex signal. At the end of the...

In the appendix B of Goldstein's classical mechanics (3rd edition), the authors discussed the dihedral group and said: "Notice how the group elements in class 3 involve only \sigma_1 and \sigma_3. Thus, they are independent of the matrices I and \sigma_2, as is expected from the structure of...

Does anyone know of a series representation for: \frac{sin(x)}{cos(x)+cosh(x)} Preferably valid for 0<x, but any ideas or assistance on any domain would be much appreciated.

For some reason, the momentum representation in QM wasn't covered in our class, so I'm figuring it out on my own (no, this isn't homework...it's just me reviewing physics for the PGRE). My question: what is the energy (kinetic energy, I guess) of a particle in the momentum representation of...

Hello, I am attempting a past exam paper in preparation for an upcoming exam. The past exam papers do not come with answers and I'm a little unsure as to whether I'm doing all of the questions correctly and would like some feedback if I'm going wrong somewhere. Any help is greatly appreciated...

Homework Statement Here it is: a particle in 1-d infinite potential well starts in state \Psi(x,0) = A Sin^{3}(\pi*x/a): 0\leqx\leqa. Express \Psi(x,0) as a superposition in the basis of the solutions of the time independent schrodinger eq for this system, \phi_{n}(x) = (2/a)^{1/2}...

Some years ago I used the device of representing composite numbers by rectangular forms to demonstrate the structure of numbers to third grade students. Primes were represented by lines of various lengths. Number 10 would be a 2x5 rectangle and 20 a 2x2x5 rectangular solid. (I used various...

Homework Statement \psi(x)=\frac{3}{5}\chi_{1}(x)+\frac{4}{5}\chi_{3}(x) Both \chi_{1}(x) \chi_{3}(x) are normalized energy eigenfunctions of the ground and second excited states respectivley. I need to find the 'wavefunction in the energy representation' The Attempt at a Solution...

Homework Statement Determine a parametric representation for the part of the sphere x2 + y2 + z2 = 4 that lies between the planes z = 1 & z = -1. Homework Equations The Attempt at a Solution We never learned spherical coordinates in class so I am not sure if I am using this...

Question in the title, ie why is Tr(T_{a_1}T_{a_2}...T_{a_n}) independent of which representation we choose, where the Ts are a matrix representation of the group generators.

What's the use of it? Anyone show a simple but illustrative example of the usefulness of representation theory? I can see how faithful representations might be useful but not fully. What I can't imagine is how unfaithful representations can be of any use. Thanks

I will soon move to Boston after living in Florida and Texas, Respectively. I was a little perturbed that I will have to pay state taxes. This was, until I found out the public school system in MA was ranked #1 and Texas and Florida #33 and #39, respectively [1]. I seem to me that the money is...

Hello everyone, This is a normal modes problem that I’m working on, where the details are a bit tedious, but what I need to do is to write the following system: mx`` = –2kx + ky + c my`` = kx – ky + c In the following form: | m 0 | |x``| = |–2k k| |x| | 0 m | |y``| =...

Hi could someone please explain the what the bloch sphere representation of a quantum state is useful for? thanks Mark

I'm trying to understand this paper which the author claimed that he had constructed an infinite dimensional representation of the su(2) algebra. The hermitian generators are given by J_x=\frac{i}{2}(\sqrt{N+1}a-a^\dagger\sqrt{N+1} ) J_y=-\frac{i}{2}(\sqrt{N+1}a+a^\dagger\sqrt{N+1} )...

I'm trying to understand this paper on the representation of SU(2). I know these definitions: A representation of a group G is a homomorphism from G to a group of operator on a vector space V. The dimension of the representation is the dimension of the vector V. If D(g) is a matrix...

Hi Guys, :smile: Can someone please explain to me the logic behind the representation of 'Magnetic Hysteresis loss' as a resistance in electrical equivalent circuits?... will be extremely grateful. I have studied some info on this subject on the net. Even though the physics of Hysteresis...

Hi Guys, :smile: Can someone please explain to me the logic behind the representation of 'Magnetic Hysteresis loss' as a resistance in electrical equivalent circuits?... will be extremely grateful. Thanks & Regards, Shahvir

Hello Everyone.I want to know if there is anything special about the position or the momentum representation in quantum mechanics.Every book deals with them.Why do not they work with Energy representation or time representation?Do not they exist?Basically,I feel it hard to imagine that a...

Hello, I hope it's not the wrong forum for my question which is the following: Is there some list of Lie algebras, whose adjoint representations have the same dimension as their basic representation (like, e.g., this is the case for so(3))? How can one find such Lie algebras? Could you...

Draw the phasor representation for each of the following signals. Also write the signal as one sinusoid, v(t) = 20cos(200t+45°)+cos(200t) From this equation, do I have to turn to v(t) = A sin (ωt + φ) ? If yes, how can I convert it? Thank you.

Dear All, I'm reading Georgi's text about Lie algebra, 2nd edition. In chap 6, he introduced "Roots and Weights". What I didn't understand is the discussion of section 6.2 about the adjoint representation. He said: "The adjoint representation, is particularly important. Because the rows...

Homework Statement Let T: P2 > P3 denote the function defined by multiplication by x :T(p(x)) = xp(x). In other words, T(a+bx+cx2) = ax+bx2+cx3 (a) Show that T is a linear transformation. (b) Find the matrix of T with respect to the standard bases {1,x,x2} for P2 and {1,x,x2,x3} for P3...

Guys, Quick one, When you do phasors for AC voltages and current... is it theVrms and Irms or can it be Vmax and Imax..? I mean the magnitude of them...I am bit confused

To any teachers or students, either instructing or taking, a Calculus-based Physics I course: I tutor a calculus-based general physics course in kinematics, and similar topics, and, I recently had a student approach me about his inability to grasp the scalar/dot product, in vector operations...

Homework Statement i) Show that the Lorentz group has representations on any space \mathbb{R}^d for any d = 4n with n = 0, 1, 2, . . .. Show that those with n > 1 are not irreducible. (Hint: here it might be useful to work with tensors in index notation and to think of symmetry...

Say I have a matrix similar to the SO(3) matrix for general 3-D rotations, except it has slightly different (simpler) elements, and the symmetry is as follows: \left(\begin{array}{ccc} A & B & C \\ B & D & E \\ C & E & D \end{array}\right) , with A, B, C, D, and E all involving somewhat...

I had a question about the following theorem. Basis Representation Theorem: Let k be any integer larger than 1. Then, for each positive integer n , there exists a representation n = a_{0}k^{s} + a_{1}k^{s-1} + ... + a_{s} where a_{0} \neq 0 , and where each a_{i} is...

In quantum mechanics, a free particle is described by a continuous superposition of wavefunctions, which can be done equivalently in real or momentum space. We can look at a particle's probability distribution in real space, take its Fourier transform, and obtain the particle's distribution in...

hey, this is my first time posting, my question is find the power series representation for x/(1-x)^2 I know the representation for 1/1-x is x^n so does that mean x/(1-x)^2 is x^n^2? could use some clarification please