Recent content by A_B

Hi, I'm confused about the discussion on p28 of Nigel Goldenfeld's "Lectures on phase transitions and the renormalization group" (this question can only be answered by people who have access to the book.) The goal is to compute the potential energy of a uniformly charged sphere where the...

Xiuh : Looks like a very interesting book, thanks for the suggestion! Joel : This idea does interest me very much. But my interest lies mainly in justifying the approximation of deterministic dynamical systems by stochastic processes. This is often done by estimating the measure of parts of...

Thanks for your suggestion, Joel. Having a quick browse, my first impression is that "Dynamics of Complex Systems" looks a lot like Strogatz's book. Very good, but not rigorous. What I'm looking for is a book that proves the theorems about convergence of Lindstedt series, birth of limit cylces...

Hi, I'm looking for a modern rigorous text on (Hamiltonian) dynamical systems, perhaps with emphasis on perturbation theory. It should be in the same vein is Poincare's "methodes nouvelles", but modern.Thanks

OK, I think I've got it. Denote by m : \mathbb{C} \times X \to X : (z, x) \to zx the scalar multiplication map. Since it is continuous and \mathcal{U} is a neighbourhoud of zero, the inverse m^{-1}(\mathcal{U}) is a neighbourhood of any pair (z, x) such that zx = 0. In particular...

Hi, There is a guided exercise in the course of functional analysis that I am following where we have to prove that a topological vectors space is seminormed if and only if it is locally convex. There is one step in te proof that I can't figure out. Let X be a topological vector space and...

As is so often the case with mathematics,the solution to the problem seems so obvious once it is known. This concludes for me a few days of staring at a blank page. Thank You, Hawkeye. You saved me a lot of time.

Hi, I'm stuck on a problem in functional analysis. Let x be a sequence on the Natural nummers such that for any square summable sequence y, the product sequence xy is absolutely summable. Then x is square summable. Hint : Use the Closed graph theorem. If I can prove the map Tx : y -> xy had a...

Looking for "Les Debuts de la Theorie Quantitique des champs" Hi, I'm not sure this is the right place to ask, but I'm looking for a text "Les Debuts de la Theorie Quantitique des champs" by Olivier Darrigol. I can't find it on the internet or my university library. thanks, A_B

Thanks for your responses. Turns out I was confused by a silly mistake. I'll use Ballentine's notation like in stevendaryl's post, because it's cleaner. The state with maximum m value is |β, j>, the state with minimal m value is |β, k> then β = j(j+1) and β = k(k-1) so j(j+1)=k(k-1). Then it...

I can't find proof that indeed |a, b_max> = (J_+)^n |a, -b_max> for some n. That is my problem

Yes, but there is no obvious reason why repeated application of J_+ on |a, b_min> should eventually reach |a, b_max>. For example, if b_max = 3.2\hbar say, then a = 13.44\hbar². The states |13.44\hbar², 3.2\hbar> and |13.44\hbar², -3.2\hbar> are eigenstates by hypothesis, and they give rise...

Hi, Both Ballentine in "Quantum Mechanics - a modern development" pages 160-162 and Sakurai in "Modern Quantum Mechanics" pages 193-196 use essentialy the same argument to show the existence of a set of eigenvectors of J² and J_z with integer spaced values of the J_z eigenvalues for fixed J²...

The Variational Principles of Mechanics - Cornelius Lanczos The Variational Principles of Mechanics - Cornelius Lanczos

Hi, I'm taking a course on Solid State Physics using this book. The reviews here and on amazon aren't very positive. Is there a good book you would suggest as a companion? Thanks, A_B