Bound Definition and 476 Threads

I'm working through an example problem wherein this bound is used: \left| \log \left( 1-\frac{1}{L^s}\right) \right| \leq L^{-\sigma}, where s:=\sigma +it and it is known that \sigma >1. How do I prove this? Should I assume the principle brach is taken?

I want to learn the definition and development of the bound polaron. Who can help me? Thank you very much!:smile:

I assume that the neutron is a particle with finite size and is <really> a single particle (that is that it does not have any further structure or components-like nucleus) and lastly it is electric nutral. I hope that these assumptions are close to the experimental observations. I am making life...

I read somewhere that quantum field theory does not allow calculations and predictions of bound states in a satisfactory way. Is that true and how much is that a problem given that qft claims to be so fundamental?

Let S = \{x | x \in \mathbb{R}, x \ge 0, x^2 < c\} Show that c + 1 is an upper bound for S and therefore, by the Completeness Axiom, S has a least upper bound that we denote by b. Pretty much the only tools I've got are the Field Axioms. I think I'm supposed to do something like: x2 \ge 0...

Hi all, we've been doing multi-variable functions and one exercise involves (or at least in the way I've been solving it) the need to bound the following from above (x and y go to infinity): \left| \frac{x+y}{x^2 - xy + y^2}\right| What I have done so far: \left| \frac{x+y}{x^2 - xy +...

Obtain an upper bound for the optimal value in the following problem; Max (4x_1 + x_2 + 2x_3 + 3x_4 ) 2x_1 - x_2 + x_3 - 2x_4 <= 2 7x_1 + x_2 + 5x_3 + 10x_4 <= 4 2x_1 + 3x_2 - x_3 - x_4 <= 2 x_i >= 0 , i= 1,2,3,4 any hint.help. please. thanks note: >= means > or equal to <= means <...

Why does the laplacian of u=0 when u is a solution to a certain boundary problem? Is this always the case?

Hi , I have some difficulties to solve this problem. It is from my numerical methods class but the problem is about taylor series: It is known that for 4 < x < 6, the absolute value of the m-th derivative of a certain function f(x) is bounded by m times the absolute value of the quadratic...

Dear members, I try to find the upper bound of the following function. Can anybody gives a hint? Thanks! f(t,p)=\sum_p \frac{p(1-p)}{t^5}[p^4(9t^4-81t^3+225t^2-274t+120)+p^3(-12t^4+129t^3-400t^2+524t-240)+ \mbox{\hspace{2cm}}p^2(4t^4-59t^3+...

hello all I know this might be a simple question to ask, but i want to find other ways of proving it anyway here we go propve that if A is a subset of R and is non empty and bounded below, then it has a greatest lower bound. This is how i did it: let b be a lower bound of A. then for...

what is basically the concept of bound charges in electrodynamics??

Especially in the early universe, what do you think would be the maximum number of stars bound in a system under mutual attraction?

Hi, I'm working on an introductory qm project, hope somebody has the time to help me (despite the length of this post), it will be highly appreciated. My goal is to determine the bound states and their energies for the potential V_j(x) =...

For the subset M in R (real numbers) If M={1+1/n : n is an element on N) then, - All upper bounds are {x:x an element of R and x > 1} - Least upper bound is 1 - All lower bounds are {x:x an element of R and x < 0} - Greatest lower bound is 0 I am not sure if I have the above...

This is Marys Peak, about 20mi west, and the highest point in the Oregon Coast Range http://home.comcast.net/~rossgr1/Maryspeak.jpg My front yard, it ought to be a lot better in a day or 2 http://home.comcast.net/~rossgr1/Magnolia.jpg The rest are just in the neighborhood...

https://www.physicsforums.com/journal.php?s=&journalid=13790&action=view Read the exctract in my journal and look at the site of the beautiful woman that discovered this bound with computer simulation... marlon

Hey guys, I have a sequence, \sqrt{2}, \sqrt{2 \sqrt{2}}, \sqrt{2 \sqrt{2 \sqrt{2}}}, ... Basically, the sequence is defined as x1 = root 2 x(n+1) = root (2 * xn). I need to show that this sequence converges and find the limit. I proved by induction that this sequence increases...

To my understanding, when a particle is in a bound state, it is "stuck" because its total energy is less than the surrounding potential. I am confused on how to prove a particular potential has no bound states. For example, in one problem, I am asked to show that there is no bound state in a...

How do I interchange the integration bound for the function below (change to dx dy): Integral from 1/2 to 1, integral from x^3 to x [f(x,y)] dy dx ?

The wavefunction for a hypothetical quantum box of size Planck length (L), when inverted through L, models the universe with this lower bound required by quantum gravitational constraints. The initial quantum box solutions are given by: \phi_n=\sqrt(2/L)\\sin(n \pi x/L) However...

What happens to a bound electron when a photon comes along but doesn't have quite enough energy to make it go up a level? What happens to the photon? Quantum mechanical and simple answers welcome.

Hello,I'm physics student.I'm from Vietnam and my English is not very good. I was wondering if anyone could help me out with a question : what are scattered states and bound states ? I'm interested in "Temperature-dependent Coulomb interation in hydrogenic systems". In this...

I need some help with a question. Q) Prove that (2n^4 + 4n^2 + 3n - 5)/(n^4 - n^3 + 2n^2 - 80) converges to 2 as n goes to infinity. A) By the algebra of limits, this converges to 2 since lim(n->oo)[2 + 4/n^2 + 3/n^3 - 5/n^4]/lim(n->oo)[1 - 1/n + 2/n^2 - 80/n^4) (2 + 0 + 0 + 0)/(1...

What makes a trajectory (orbit) bound?

I was recently reading an article about how quantum computer scientists have found a way to infuence the spin of electrons, http://www.aip.org/enews/physnews/2002/split/595-2.html, My question is, I know that for instance, if two electrons were in the same atom of ground state He, the...