Hi Mr-R,
thanks for your answer. Yes, but my problem is that the sum is not running over r_i but over i.
Let's assume the r_i are an set of positions, for example always the same position, i.e. r_i={1,1,1,1,1,1,....}. Then in the end, that's just a product
prod_n=0^\infity e^{i(k-q)}
Best,
Hey all,
i've found the following expression:
How do they get that? They somehow used the kronecker delta Sum_k exp(i k (m-n))=delta_mn. But in the expression above, they're summing over i and not over r_i??
Best
Hey all,
I got some question referring to the interaction picture. For example:
I have the Hamiltonian ##H=sum_k w_k b_k^\dagger b_k + V(t)=H1+V(t)##
When I would now have a time evolution operator:
##T exp(-i * int(H+V))##.
(where T is the time ordering operator)
How can I transform it...
Thanks! :)
but then I'm a bit confused. For example, when I have a look at the D_n group and the representation of it.
http://groupprops.subwiki.org/wiki/Linear_representation_theory_of_dihedral_groups
I know that this representation is irreducible but I could diagonalize all of these...
Hey,
thanks for your answers! :)
I'm not actually sure if I understand this right.
Does block-diagonalizability implies diagonalizability or is it the other way round?
Best regards :)
Hey folks,
I'm trying to dip into group theory and got now some questions about irreducibility.
A representation D(G) is reducibel iff there is an invariant subspace.
Do this imply now that every representation (which is a matrix (GL(N,K)) is reducibel if it is diagonalizable?
Best regards
Hey Shyan,
thanks for your answer. I tried to find the maximum by using the Lagrange function, so:
L=|a|^2 A_11 + |b|^2 A_22 +a b* A_12 +b a* A_21+lambda(a^2 + b^2 - 1)
Now I got the problem that I don't know how derive L w.r.t c* (conjugated c). I also think that there is a better way to...
Homework Statement
I have a hermitian Operator A and a quantum state |Psi>=a|1>+b|2> (so we're an in a two-dim. Hilbert space)
In generally, {|1>,|2>} is not the eigenbasis of the operator A.
I shall now show that the Eigenvaluse of A are the maximal (minimal) expection values <Psi|A|Psi>...
Hi,
thanks for your answer :-)
I'm still a bit confused. Let me summary again what I have:
Two electrons characterized by a wave vector k, where I know that the normalization is :<k|k'>=(2Pi)^3 Delta(k-k').
Now I have the state |k1,k2> and I shall construct the space wave function.
My...
Hi,
I want to calculate the position-wave-function of a system of two free electrons with momenta k1 and k2 (vectors).
1. Homework Statement
So, I want to have Psi_(k1,k2)(x1,x2) for a state |k1,k2>
I also know that <k'|k> = (2Pi)^3 Delta(k-k')
The Attempt at a Solution
I tried the...
Hi,
I should Show the following:
D is subset of R^2 with the triangle (0,0),(1,0),(0,1). g is steady.
Integral_D g(x+y) dL^2(x,y)=Integral_0^1 g(t)*t*dt
my ansatz:
Integral_0^1(Integral_0^(1-x) g(x+y) dy) dx
With Substitution t=x+y
Integral_0^1(Integral_x^1 g(t) dt) dx...
Hi,
thanks for your answer. I think they should all have primes.
Edit: I should only calculate the potential A(r) on the z-axis (for r=z e_z). But I dont know how this can be helpful.
Homework Statement
Hey,
I got the current density \vec{j}=\frac{Q}{4\pi R^2}\delta(r-R)\vec{\omega}\times\vec{r} and now I should calculate the vector potential:
\vec{A}(\vec{r})=\frac{1}{4\pi}\int\frac{j(\vec{r})}{|r-r'|}.
Homework Equations
The Attempt at a Solution
here my attempt...
Homework Statement
I got the the radial part of the Laplace-Equation:
r^2(\frac{d^2}{dr^2}U(r))=l(l+1)U(r)
Now I should show that the following solves the equation:
a_l*r^l+\frac{b_l}{r^l}
The Attempt at a Solution
The problem is that I got l(l-1) instead of l(l+1) :(