Recent content by Faust90

1. I Kronecker delta by using creation/annihilation operators

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,
2. I Kronecker delta by using creation/annihilation operators

Do you need more background or is the question not precise enough? :-)
3. I Kronecker delta by using creation/annihilation operators

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
4. Interaction picture - time evolution operator

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...
5. Virial Theorem

Hey guys, I was wondering if i can use the virial theorem for a potential of the form V(x)=A*|x| Got some trouble at the point x=0. Best regards
6. Group theory - beginner

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...
7. Group theory - beginner

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 :)
8. Group theory - beginner

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
9. Hermitian Operators Eigenvalues

Thank you very much! :-)
10. Hermitian Operators Eigenvalues

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...
11. Hermitian Operators Eigenvalues

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>...
12. Position wave function of two electrons

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...
13. Position wave function of two electrons

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...
14. Triangle with Fubini

Hi, thanks for your answer :) One of my favorite quotations. I think I got it. If somebody want, i can write the solution here. Greetings
15. Triangle with Fubini

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...