Representation Definition and 766 Threads

Whenever you see representations of gravity in terms of relativity, you see a planet sitting on a 2d surface of fabric (space) and it is making an indentation, almost as if there another source of gravity pulling it downwards against the fabric. I think this is a poor representation. I mean...

p=\hbar k So ##dp=\hbar dk## How to define Fourier transform from momentum to coordinate space and from wave vector to coordinate space? I'm confused. Is there one way to do it or more equivalent ways?

Coordinate representation ##\psi=\psi(x)## Momentum representation ##\psi=\psi(p)## Fourier transform \psi(p)=\frac{1}{\sqrt{2\pi\hbar}}\int^{\infty}_{-\infty}\psi(x)e^{-\frac{ipx}{\hbar}}dx I'm confused with this ##\hbar##? Why not...

Hi there, eI have two numbers: z1 = 2 + i z2 = exp(iδ) * z1 i are complex numbers and δ is a real number. I need to answer a question - what does the graphical representation of z2 have in relation to the graphical representation of z1. Thanks for any help!

Homework Statement Use differentiation to find a power series representation for f(x)=1/(1+x)2 Homework Equations The Attempt at a Solution 1/(1-x) = \sum(x)n 1/(1-(-x)) = \sum(-x)n Deriving 1/(1-(-x)) -1/(1-(-x))2= \sumn(-x)n-1 from n=1 to infinity indexing it from...

Homework Statement How can I get to that answer? Homework EquationsThe Attempt at a Solution I'm stuck don't know how to get to the answer that I got from wolframalpha. there is no solution there unfortunately. I know how to get to that denominator w^2-1 but I don't know how to get to...

Can anybody please tell me how to represent a neutral antimatter body such as a planet or a star in the classical formulation of special and general relativities? Thanks.

[EDIT]: Correct answer for this problem is 1/2, not 4 as I thought before; that means the result for the explicit representation was correct. Still I don't understand how to treat the case with the parametric representation. Greetings, I need to evaluate $$\iint_{S}\mathbf{F}\cdot\mathbf{n}\...

Homework Statement write a power series representation of the following: \frac{x}{15x^2 +1} Homework Equations the formula \frac{1}{1-x} = 1 + x + x^2 + ... = \sum_{n=0}^{∞} x^n The Attempt at a Solution we can rewrite the summnd like \frac{x}{15} \left(...

Heyy! Please check the attachment and explain why are they arranged (the matrix entries) the way they are? I mean, what is the rule for building up a matrix? In other words, why did not we start with <-1/2, -1/2 l S^2 l -1/2, -1/2 > and placed it as being the first entry? Thanks.

Hi guys, I was studying the proof below and just can't figure out the the first highlighted step leads to the second and I was wondering if you guys can help me to fill that in. (: Thank you so much for your help in advance guys!

We were told in lectures that the time independent Schrodinger equation can be applied to wavefunctions, i.e. \frac{hbar^2}{2m}\frac{d^2U}{dx^2}+V(x)U=EU where U is the wavefunction bra x ket psi. I don't understand why this is valid, as wavefunctions are probability amplitudes, and operators...

In Mark Srednicki's book "Quantum Field Theory" He says that a tensor field B^{αβ} with no particular symmetry can be written as :- B^{αβ} = A^{αβ} + S^{αβ} + (1/4) g^{αβ} T(x) Equn. 33.6 where A - Antisymmetric, S = symmetric and T(x) = trace of B^{αβ} . Is there any reason...

Homework Statement I am trying to represent the function 2x/(1+x2) as a series and determine its radius of convergence. Homework Equations The Attempt at a Solution Using the series for ln(1-x) I have come up with the following series: Ʃ(n=1,infinity) [2*(-1)n*x2n-1], with radius...

I have a question that is a little hard to explain, since i don't know the name of this method, but I'll try my best, if anyone knows the name please do tell me. So let's say we have three numbers, 1 2 3 (in this order) and we have a container for this numbers: C123 and we have some...

The Fourier series of a delta train is supposedly (1/T) + (2/T ) Ʃcos(nωt) ... where T is period and ω=2*Pi/T ...but when I plot this, it doesn't give me just a spike towards positive infinity, but towards negative infinity as well (see attached pic), so this does not seem to converge to the...

What do we mean by 'Equivalent Projective representation"? I know that we say two representations R and R' of a group G is equivalent if there exists a unitary matrix U such that URU^(-1)=R'. But what do we mean by equivalent projective rerpesentations? I've heard of the theorem that the...

Consider continuous function x(t), which has zero time average: \lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{T/2} x(t)\,dt = 0 and exponentially decaying autocorrelation function: \lim_{T\rightarrow\infty}\frac{1}{T}\int_{-T/2}^{T/2} x(t)x(t-\tau)\,dt = C_0e^{-\gamma |\tau|}...

How do I go from the entropy of a system, S(U,V,N), to its internal energy, U(S,V,N)? For instance, for an ideal classical gas, we have S=(3/2)N*R*ln(U/N) + N*R(V/N) + N*R*c where R is the Boltzmann constant, N is the particle number, V is the volume and "c" is a constant. How can I...

Homework Statement I have my quantum mechanics final creeping up on me and I just have a question about something that doesn't appear to be covered in the text. Let's say you have a wave function of the following form for a linear harmonic oscillator: \Psi = c_1 | E_1 \rangle + c_2 | E_2...

Homework Statement Represent 5x / (10 + x) as a power series, find c0, c1, c2, c3 and c4, find the radius of convergence The Attempt at a Solution I think I got the representation fine: Ʃ from 0 to ∞ = 1/2 [ (-1^n)(x^n+1) / 10^n ] Radius of Conv. = 10 But what the hell are those...

Is this interesting? I have a way to represent all of the real numbers with a subset of the open interval (0,1). I write as a binary decimal x = .a_{0}a_{1}a_{2}a_{3}... where x = \sum -1^{a_{0}+1}/p_{i} where p_{i} is the i^{}th prime. Since the reciprocals of the primes diverges, in this...

Homework Statement I think I've done (a) and (b) correctly (please check). I'm stuck as to how to describe all subspaces of V that are preserved by the operators \varphi(t) and how to prove that \varphi can't be decomposed into a direct sum \varphi = \varphi |_U \oplus \varphi |_{U'}...

Hello, Typically the area of a parallelogram if give by A=b*h The det(M) =ad-bc, where m=2x2 matrix. How they are related? -- Shounak

Hello all, Recently I've found something very interesting concerning Taylor series. It's a graphical representation of a second order error bound of the series. Here is the link: http://www.karlscalculus.org/l8_4-1.html My question is: is it possible to represent higher order error bounds...

Homework Statement I am asked to find a power series for the function f(x) = 2/(1 - x^2), centered at 0. Homework Equations The Attempt at a Solution The only part I can't determine is the interval of convergence. I get stuck on the step |x2| < 1. What am I to do next?

Hello Forum, When we represent a vector X using an orthonormal basis, we express X as a linear combination of the basis vectors: x= a1 v1 + a2 v2 + a3 v3+ ... Each coefficient a_i is the dot product between x and each basis vector v_i. If the vector x is not a row (or column vector)...

Homework Statement Write an iterative program to find the largest integer n such that the equation 6a + 9b + 20c = n where a, b, c are nonnegative integers, has no solution.Homework Equations We are given that the set of n in {x, x+1, x+2, ..., x+5} has nonnegative solutions a, b, c to the...

Homework Statement I need to verify an integral representation of the Euler constant: \int^{1}_{0}\frac{1-e^{-t}}{t}dt-\int^{\infty}_{1}[\frac{e^{-t}}{t}dt=\gammaHomework Equations The Attempt at a Solution OK, I'm supposed to use this fact (which I have already proved)...

Homework Statement O hai, my minions. So...we made the xantoprotheic reaction in the lab, but I have to attach the representation of the reaction. I haven't found it anywhere. So I came to you. Homework Equations Protein + NaNO3→(180s@373K)→(room temp) + NaOH→ Weird yellow precipitate...

Hello, everyone. I understand the Standard Model and all of its quarks, leptons and bosons, but could someone show me the equation and simply explain it? I haven't been able to find it or an explanation of how it relates to the graphical representation of the Standard Model. Thanks in advance!

I've used many different power series representations of functions and seem to always take it for granted that functions which are "nice" and continuous have such a representation. But what is the criteria for a function to have a power series representation? I know of some that don't, but...

The solution to a linear differential equation is, y=exp(ax). If a is complex ,say a=b+ic, then the period is T=2pi/c. My question is, if a is in polar form, a=r*exp(iθ), how is the period then T=2pi/θ. Any help would be great, Thank, Will

Homework Statement The quantum numbers +1/2 and -1/2 for the electron spin represents? Homework Equations a) rotation of electron in clockwise and anticlockwise directions respectively b) tow quantum mechanical spin states which have no classical analogue c) Magnetic moment of electron...

I've been trying to do the following question but I can't get the right answer. Also, I put in the wrong thread title but I don't know how to change it (sorry). An ambulance is at rest in a traffic jam in front of an intersection. At that moment, Jim is driving his car at 88.0 km/h through the...

Homework Statement I'm having trouble understanding a concept in representation theory. I've been reading several texts on the application of rep. theory to quantum mechanics ("Group Theory and Quantum Mechanics" by Tinkham and "Group Theory and Its Application to Physical Problems" by...

I know how to use determinants to solve a system of linear equations, I know I can use them to find the rank of a matrix and find out if a system is linear dependant/independant. However, I still don't really "get" determinants. To me they're some sort of magic box that I can use to calculate...

I'm self-studying representation theory for finite groups using "Group Theory and Quantum Mechanics" by Michael Tinkham. Most of it makes sense to me, but I'm having difficulty understanding what is meant by saying a function "belongs to a particular irreducible representation", or "has the...

It seems that there’s a loose way of discussing group representations that’s fine for the initiated, but confusing for the neophyte: I understand that the objects that represent group operations are usually (or always?) square matrices, which naturally can be described as “matrix...

Hi, I have the following problem, I have an electric field (which no charge) which satisfies the usual Laplace equation: \frac{\partial^{2}V}{\partial x^{2}}+\frac{\partial^{2}V}{\partial y^{2}}+\frac{\partial^{2}V}{\partial z^{2}}=0 in the region \mathbb{R}^{2}\times [\eta ,\infty ]. So...

Dear forum members! Could someone tell me a reference, where it is accurately described how the SM particles + right-handed neutrino are assigned to the \overline{16} representation in SO(10) models? I mean: Which component of the particle vector represents which particle? Mainly I am...

Could you advise a DSP book which explains state-space representation with initial conditions. Initial conditions part is important for me. Thanks.

The position operator in coordinate representation is: Xab=aδ(a-b) this is diagonal as expected The momentum operator turns out to look like Pab=-ih∂aδ(a-b) Now, this is not supposed to be diagonal because it does not commute with X. However it looks pretty diagonal to me. What am I...

I'm thinking of expanding the numerical value of a real number in different bases. I want you guys to ensure some things for me so I know I'm not wrong. If X is the representation of a in the base B and Y is the representation of b in the same base(radix), can we say that X+Y = a+b? In...

Please forgive such a simple question, but how does a particle 'remember' what direction to travel in from instant to instant? I mean, say we take 2 particles way out in space, we kick one say along a +x axis, and the other with the same force along the -x axis... How is the Direction...

hi, is it misleading to write omega = 1.0000... for the ideally flat space?

I am trying to prove a specific representation of Euler's constant, but I am not really getting anywhere. I hoped you could help me with this one, because I looked it up on the Internet and even though the relation itself is found in many webpages, its proof is in none. The relation is...

Homework Statement I am calculating the corrections to the beta functions of a quite general SU(N) gauge-yukawa theory coming from coupling an electro-weak (SU(2)xU(1)) sector similar to that of the Standard Model. To do this, I need to calculate...

Do Lorentz Transformations or their products having irreducible representation, and is superposition allowed or special consideration are needed?

The general evolution of a ket |\psi\rangle is according to -i\hbar\frac{d}{dt}|\psi\rangle=H|\psi\rangle without specifying a representation. From this equation, how can you simply get a equation in a certain representation F as below: -i\hbar\frac{\partial}{\partial t}\langle...