Bound Definition and 501 Threads

So far, we've discovered this compositeness hierarchy: Atoms - bound states of electrons, nuclei, photons Nuclei - bound states of nucleons and other hadrons Hadrons - bound states of quarks and gluons So are any Standard-Model particles bound states of any other particles? The...

I'm trying to find a value K>o such that for real a,b,c,d (a^2+c^2)x^2+2(ab+cd)xy+(b^2+d^2)y^2 ≤ K(x^2+y^2). Any help on this would be greatly appreciated thanks.

I've thought about dark matter and I'm wondering if it could possible be made up invisible bouond states of ordinary matter? Wikipedia says "According to consensus among cosmologists, dark matter is composed primarily of a new, not yet characterized, type of subatomic particle." But why a...

Homework Statement Consider the semi-infinite square well given by V(x) = -V0 < 0 for 0≤ x ≤ a and V(x) = 0 for x > a. There is an infinite barrier at x = 0 (hence the name "semi-infinite"). A particle with mass m is in a bound state in this potential with energy E ≤ 0. Solve the Schrodinger...

Use the delta-epsilon definition to prove f(x,y) = y/(1+x2) is continuous at (0,0)Attempts:So I'm doing some work and my main issue is finding a bound for the denominator of 1+x2: So work wise I have something looking like: \delta/(|1| + |x2| ). How could I found a good bound?

Hii everyone, Can anyone tell me a decent upper bound of Ln[x](which can mimic Ln[x]) where x is in [0,1]regards, Bincy

"higher" bound state just a quick question on terminology.. if something has a higher binding energy, can it be said to be in a higher bound state? thanks

Hi :), recently I was thinking whether every bound state is only real or imaginary, not mixture? Since all bound states have degeneracy of level one, if we suppose that ψ=ψ_{r}+iψ_{i}, then ψ_{r} and ψ_{i} must be linearly dependent as in opposite case there would be a bound state with...

In my chapter about electric fields in matter my book derives and expression for the potential due to the polarization of a dielectric material. For that you find that the polarization is equal to the potential of a collection of negative charges on the surface and positive charges inside the...

Homework Statement I'm just trying to understand better what happens at the interface between a conductor and a dielectric, particularly with regard to free and bound charge. I would like to know: - under what conditions can a dielectric acquire free charge, and how this free charge...

Upon reading about bound charges I stumbled on something I didn't quite understand. It is not a physical thing but purely a mathematical thing. In the attached section my book wants to take the gradient: ∇'(1/r) with respect to the source coordinates, r'. Now, can someone by inspection...

Hello, I have the following determinant: \text{det}\left(\mathbf{A}\mathbf{A}^H\right) where H denoted complex conjugate transpose, and A is a circulant matrix. I am looking for a lower bound for the above determinant. Is there one? Thanks in advance

Greetings. Let's say we have a bound state problem: two micro black holes in orbit around one other. Let us disregard Hawking evaporation, and solve this problem. The usual way of solving this problem is to do so quantum-mechanically by employing the Schrodinger equation, deducting the...

Can anyone suggest an upper bound for e^{-x^2} that can be integrated easily?

Hello, I have this quantity: \frac{1}{\sum_{m=1}^NX_m^{-1}}\geq\frac{1}{N\underset{m}{\text{max }}X_m^{-1}}=\frac{\underset{m}{\text{min}}X_m}{N} Is that true?

In non-relativistic QM, we spend a lot of time examining bound states--energy levels, spatial distributions, and all that. We can determine that an electron put into a Coulomb potential will have certain Hamiltonian eigenstates, which correspond to the orbitals of a hydrogen atom. However, in...

Find the error bound of approximation of f using the cubic spline want to find a cubic spline for f on the interval [a,b] suppose we have n nodes with n-1 different intervals I tried to find it using the Taylor expansion around any nodes say x_i \in [a,b] f(x) - S(x) = f(x_i)-S(x_i) +...

Hi, Despite decades of searching magnetic monopoles haven't been found. Could it be that they are existing as bound states of a North and South monopole? One could model such states as a Bohr atom. It seems that the ground-state binding energy would be much more negative than the...

I often hear something to the extent of, 1) "despite cosmological expansion, small-bound objects do not expand." and further, 2) "things like galaxies will aways remain bound, and will not expand." Pertaining to 1) Because cosmological expansion is a coordinate property, don't small scale...

The definition of 'Bounded above' states that: If E⊂S and S is an ordered set, there exists a β∈S such that x≤β for all x∈E. Then E is bounded above. The 'Least Upper Bound Property' states that: If E⊂S, S be an ordered set, E≠Φ (empty set) and E is bounded above, then supE (Least Upper...

Homework Statement I'm dealing with a dirac particle in an attractive spherical square well. I've solved for the transcendental equation to find energy, found the normalized wave function, and now I'm trying to explain what happens when the well becomes very deep, when V0 ≥ 2mc2. If I plug...

Free particle --> bound particle Homework Statement A free neutron meets a finite square well of depth V_{0}, and width 2a centered around origo. However, the probability that the neutron emits a photon when it meets the potential well, and thus decreasing its energy is proportional to...

Homework Statement For the following set if it has an upper bound, find two different upper bounds as well as the least upper bound (LUB), justifying your answer. If the set has no upper bound, state this and justify your answer. {x | 1 < x < √(7) and x is irrational} (a proof requires the...

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

Dears, If a random variable is generated with the pdf of p(f) = 1/(f^x), how can I derive the upper bound or lower bound of the random variable? Thanks,

I see equations of the form, y=\int_{-\infty }^{t}{F\left( x \right)}dx a lot in my texts. What exactly does it mean? From the looks of it, it just means there is effectively no lower bounds. I looked up improper integrals, but I can't say I really understand what is going on. So when...

Is there a theoretical upper bound for the density of matter? Given a proton (already almost as dense as a black hole, according to Wikipedia), can you theoretically compress it into any non-zero volume? Has any work been done that shows that matter can or cannot achieve certain levels of...

Homework Statement Use the Archimedean property of \mathbb{R} to prove that the greatest lower bound of {\frac{1}{n}:n\in\mathbb{N}}=0 the archimedean principle says that for any number y there is a natural number such that 1/n<y for y>0 The Attempt at a Solution since all of...

Homework Statement Hi, I just have a basic question regarding an asymptotic tight bound question. The question is : TRUE / FALSE http://latex.codecogs.com/gif.latex?3^{n+1} \text{ belongs to } \Theta(3^{n}) By definition of big theta: c_{1}g(n) \leq f(n) \leq c_{2}g(n) \text { }...

Why doesn't a dineutron system form a bound state? Why doesn't 2 neutrons with one spin up and the other spin down form a bound state but a neutron and proton with both spin up or down form a bound state

Homework Statement Give an example of a bounded subset of Q which has no least upper bound in Q. Explain why your answer has this property. Homework Equations The Attempt at a Solution [1/8, 1/4, 3/8, 1/2, 5/8, 3/4...infinity] is this correct?

Hello I'm trying to show that the following upper bound on the matrix 2-norm is true: \left\|(AB)^+\right\|_2\leq\left\|A^+\right\|_2 \left\|B^+\right\|_2 where + is the matrix pseudoinverse and A\in\Re^{n\times m} and B\in\Re^{m\times p} are full-rank matrices with n\geq m\geq p...

Hi all, I would like to understand the mechanism by which a neutral impurity can bind an exciton. Because the impurity is neutral the attracation can not be simply electrostatic. I know that there must be a "neutralising electyron (or hole)" in the machanism but things are not clear enough...

This calc book that I am reading uses words like "upper bound" and "sup" a lot when proving theorems. I have never heared these terms before so it makes it hard for me to understand the proofs. I think it has to deal with max's values of a graph: For example given a set S of all elements c in...

Homework Statement Consider a particle with mass m and angular momentum l in the field of a central force F=\frac{-k}{r^{5/2}}. To simplify your equations, choose units for which m=l=k=1. a) find the value r_{0} of r at which U_{eff} is a minimum and make a plot of U_{eff}(r) for 0<r<5r_{0}...

Homework Statement I'm trying to learn the Branch and Bound method. For that, I need to master the Dual Simplex Method (DSA). I have tried and tried and tried to google examples but can't find any. Does anyone know where I can find any? How do you know the LPP has become infeasible with...

Homework Statement So I have been given an algorithm that solves this problem. However, the aim was to make it faster and I have done this. The problem is I fail to explain why it has made the algorithm faster. It's more of a math problem which I haven't understood. I solved this through trail...

I am looking for a bound for the following expression S=\sum_{n=1}^N n^k e^{-an} where a>0 and k=1, 2, 3, or 4, apart from the obvious one: S\le \frac{n+1}{2} \sum_{n=1}^N e^{-an} = \frac{n+1}{2} \frac{1-e^{-Na}}{e^a-1}

Homework Statement I'm given that the function f(x) is n times differentiable over an interval I and that there exists a polynomial Q(x) of degree less than or equal to n s.t. \left|f(x) - Q(x)\right| \leq K\left|x - a\right|^{n+1} for a constant K and for a \in I I am to show that Q(x)...

Salutations! Just checking if my logic is correct. Homework Statement I need to bound the error for \tan x on [0, \frac{\pi}{2}] Homework Equations R_n(x) = \displaystyle \frac{\tan^{n+1}(\zeta)}{(n+1)!}x^{n+1} The Attempt at a Solution So...I thought that the error...

Homework Statement An infinitely long cylinder, of radius R, carries a frozen-in magnetisation, parallel to the z-axis, M=ks k-hat, where k is a constant and s is the distance from the axis. There is no free current anywhere. Find the magnetic field B inside and outside the cylinder by two...

Homework Statement A current I flows down a long straight wire of radius a. The wire is made of linear material with susceptibility chi(subscript m), and the current is distributed uniformly. i) what is the magnetic field a distance s from the axis? ii) Find all the bound currents. What...

I have the following question: Let n\in\mathbb{Z}^{+} st. n is not a perfect square. Let A=\{x\in\mathbb{Q}|x^{2}<n\}. Show that A is bounded in \mathbb{Q} but has neither a greatest lower bound or a least upper bound in \mathbb{Q}. To show that A is bounded in \mathbb{Q} I have to show...

Homework Statement a) Prove that \ell_\infty \mathbb({R}) is a subspace of \ell \mathbb({R}) b) Show that \left \| \right \|_\infty is a norm on \ell_\infty (\mathbb{R}) The Attempt at a Solution For a) I guess we have to show that \vec{x} + \vec{y} \in \ell_\infty \mathbb({R})...

Homework Statement A particle moves in one dimension in the delta function potential V= αδ(x). (where that is an 'alpha' ... not 'a') An initial wave function is given \Psi = A(a^2-x^2) for x between -a and a and Psi=0 anywhere else What is the probability that an energy measurement will...

Hello all, the problem I have is the following: Suppose f \in C^1(0,1) and f(0) = 0, then f^2(x) \le \int_0^1 f^2(x) dx, but I was wondering if 1 is the best constant for the inequality. In other words, how do I determine the best bound for f^2(x) \le K \int_0^1 f^2(x) dx...

Homework Statement Problem as written in text (Eisberg, 2nd): If a particle is not bound in a potential, its total energy is not quantized. Does this mean the potential has no effect on the bahavior of the particle? What effect would you expect it to have? Homework Equations The...

Homework Statement Use part (a) to prove the Greatest Lower Bound Property. (a): If M is any upper bound for A, then: x\in(-A), -x\inA, and -x\leqM. Therefore x\geq-M, hence -M is a lower bound for -A. By the Least Upper Bound Property, inf(-A) exists. If inf(-A) exists, then...

upper bound of taylor! f(x) is two times diff. function on (0, \infty) . \lim\limits_{x\rightarrow \infty}f(x) = 0 satisfy. M=\sup\limits_{x>0}\vert f^{\prime \prime} (x) \vert satisfy . for each integer L , g(L) = \sup\limits_{x\geq L} \vert f(x) \vert, and h(L) = \sup\limits_{x\geq L} \vert...

I prefer to give investigators the benefit of the doubt, always, but I'm having a really hard time going along with this one. Beware that the link has a censored photo of the body from a distance in the air, and may upset some sensitive individuals...