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    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
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    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...
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    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
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    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
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    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>...
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    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...
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    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...
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    Vector potential with current density

    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...
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    Solution of the radial part of the laplace-equation

    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) :(