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?
Homework Statement
Homework Equations
Suppose we have a single qubit principal system ,interacting with a single qubit environment through the transformation
U=P0\otimesI+P1\otimesX
where X is the usual Pauli matrix (acting on the enviornment)and P0=|0><0| ,P1=|1><1| are projectors...
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+,a_, and a+a-
All of these operators are supposed to operate on Hilbert space, and be represented by m*n matrices.
Homework Equations
a+=1/square root(2hmw)*(-ip+mwx)
a_=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 a0 denote the largest...
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...
Homework Statement
What is the range of a 11bit code, using
c. Unsigned fixed-point with 8 binary places
Homework Equations
Base conversions
2^n where n is bits, for range/precision
The Attempt at a Solution
I have two ideas:
1)
The highest value that can be represented is...
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...
Find the parametric representation for the surface:
The part of the sphere x^2 + y^2 + z^2 = 16 that lies between the planes z = -2 and z = 2.
okay, i know that i have to use spherical coordinates which is
x = 4sin(phi)cos(theta)
y = 4sin(phi)sin(phi)
z = 4cos(phi)
i know how to find...
F(x,y,z)=(-\frac{y^2+2z^2}{x^2},\frac{2y}{x},\frac{4z}{x})
"Find parametric representations of the field lines."
How do I parametrize all possible field lines?
I think I will write out the beginnings of a "book" that I'd been meaning to get around to starting at some point. Better that someone might actually read it here than trust to them finding it on my web page.
Any requests, let me know by PM (or if this is inappropriate for this forum)...
Does anybody know whether the following irreducible representations of SU(2) are unitary?
g belongs to SU(2)
[U_j(g) f](v) = f(g^{-1} v)
f is an order-2j homogeneous complex polynomial of two complex variables v = (x, y)
e.g. for j = 1, f = 2x^2 + 3xy + 4y^2
Can please explain to me what a representation of a group is please?
Hopefully something more illuminating than what I might find on wikipedia or eric weissteins mathworld.
Also, perhaps illustrated with an example.
I see this term a lot. I know its something to do with a group but I'm not too sure what it is.
Also - how does a representation (mathematical concept) translate into particle physics concept.
I am reading ahead for my Group Theory introduction to QFT and I have a question about the dual representation. If the dual representation is the same as the ordinary representation, that is to say the ordinary representation is "real", how do we represent anti-particles in this case? This...