Bound Definition and 476 Threads

Homework Statement 1. (a) Solve the following inequalities and express the solutions first in interval notation, then express those intervals in set builder notation. (i) x3 + x2 > 2x (ii) \left|(2-x)\right| \leq 4 . (b) For each of the solution sets in part (a), state the least upper...

Homework Statement A bound quark-antiquark pair is a ________ while a bound quark triplet is a ________ Homework Equations The Attempt at a Solution I think that a bound quark-antiquark pair is a baryon while a bound quark triplet is a meson. Where can I find a mathematical...

Say we have a proton and a neutron. How can we get them bound to form a deuteron? If the neutron is still in the lab's framework, we bombard it with protons with such a kinetic energy that they can form a deuteron with the neutrons. But if we look at the potential of the nuclear force between...

Homework Statement assume that x and y are vectors, and A is a matrix. can anyone kindly help me to find an upper bound C w.r.t \| A \| s.t. \| x-Ay \| \leq C \cdot \| x-y\|

1) "Least upper bound axiom: Every non-empty set of real numbers that has an upper bound, has a least upper bound." Why does it have to be non-empty? Is there an upper bound for the empty set? 2) "It can be proved by induction that: every natural number "a" is of the form 2b or 2b+1 for...

http://www.cnn.com/2009/WORLD/europe/12/30/airline.terror.schiphol/index.html" Amsterdam's Schiphol Airport will start using full body scans for US bound flights. I remember seeing this technology in its early stages a few years ago and remember the privacy issues. I am glad to see it...

Homework Statement Determine a lower bound for the radius of convergence of series solutions about a) x_{0}=0 and b) x_{0}=2 for \left(1+x^{3}\right)y''+4xy'+y=0. Homework Equations N/A The Attempt at a Solution The zero of P\left(x\right)=\left(1+x^{2}\right) is -1. The...

Can anybody recommend a good review article (or a book) for bound state calculations in QFT? I have never seen anything along these lines, other than brief sections or paragraphs in various textbooks about the connection to the Schrodinger equation in the non-relativistic limit for two particle...

This is not a homework problem, just a question I encountered I thought I should figure out. Homework Statement ....__... _______ ..._____...|..|_ ..|-------------Energy ....|_|...|_| ...A...B.C.D..E...FEdited due to formatting of my picture. Please ignore the periods I had to use them to...

Homework Statement A conducting wire carrying a charge \lambda per unit length is embedded along the axis of the cylinder of Class-A dielectric. The radius of the wire is a; the radius of the cylinder is b. Show that the bound charge on the outer surface of the dielectric is equal to the...

Least Upper Bound proof... Homework Statement Suppose A is a nonempty set that has x as an upper bound. Prove that x is the least upper bound of the set A iff for any E>0 there exists a y in A such that y>x-E Homework Equations None The Attempt at a Solution The forward where you...

if f is continuous on [a,b] with f(a)<0<f(b), show that there is a largest x in [a,b] with f(x)=0 i think it can be done by least upper bounds, but i dun know wat is the exact prove.

Homework Statement Find an upper bound M for f(x) = |x-2 / x+(1/2)| if |x+1| < 1/4 Homework Equations The Attempt at a Solution I'm confused about this |x+1| < 1/4. Does this mean that |x-1| < 1/4? |x-2/x+(1/2)| = x-2/(2x+1)/2 = 2(x-2)/(2x+1) = 2x - 4/2x + 1 = x-2/x+(1/2) <...

What is meant by total negative energy associated with bound bodies like planets. and also total energy of the hydrogen atom is negative. I wonder how it could be? Because I believe whatever negative energy may be, It must only be associated with bound systems, and I don't think that an isolated...

A railroad car that weighs 20,000 lbs. is traveling eastward with a velocity whose magnitude is 5 ft./sec. A second car, on the same track, that weighs 40,000 lbs. is also traveling in an easterly direction with a velocity of 7.81 ft./sec. When the cars collided, they became coupled together...

Homework Statement Use the completeness axiom to prove that to prove that every non-empty subset of real numbers, which is bounded below, has a greatest lower bound. Homework Equations N/A The Attempt at a Solution Assume A is a nonempty subset of real numbers which is bounded...

Homework Statement Assume that A and B are nonempty sets, that A is bounded above, and that B is contained in A. Prove that B is bounded above and that the least upper bound of B is less than or equal to the least upper bound of A. Homework Equations Definition: Least Upper bound: Let...

The author of my calculus book defines an "almost upper bound" as follows: A number x is an almost upper bound for the set A if there are only finitely many number y \in A with y \geq x. He then asks the reader to prove that if A is a bounded infinite set, then the set B of all almost upper...

Say I have a container with room for B balls. I know that there are black and white balls but I don't know the ratio between them. Say I pick P balls, and R% are black. How can I use this information to establish an upper bound on the number of white balls, with C% certainty? To give a...

Hello all, This may be my very first post on Physics Forums. I am a 1st year physics grad student and need some help on something that's been bugging me. Suppose we have two spin half particles in a bound state. The total spin will either be 0 or 1. The spin 0 state, for example, would be...

I was thinking about bound and unbound states the other day and want to know: Is unboundedness a requirement for a traveling wave? That is, if you were to build a beams from bound states, would they become standing waves?

I read the following: "If {T_i} is a non empty family of topologies on our set X, then the least upper bound of this family is precisely the topology generated by the class \bigcup T_i; that is, the class \bigcup T_i is an open subbase for the least upper bound of the family {T_i} ." I...

there are n balls of weight 1/n. an opponent choose each time a subset of balls that each one has weight less than 1. then each ball in this set, its weight is multiplied by 1+\frac{1}{|S|} where S is the set of balls that the opponent chose. I need to show that for each choice of subsets...

Homework Statement v=3 Is v a free or bound variable? The Attempt at a Solution Bound to me since we can see it as there exists v such that v=3.

I'm wondering if a gas in which all its molecules are moving very close to the speed of light has a finite temperature. More precisely, if we take the limit of the speed of the particles to be exactly the speed of light (I know it's impossible to reach, but as I'm calculating an upper bound I...

Homework Statement We know that a sphere of radius R carries a polarization P(r)=kr where k is a constant and r the vector from the centre. Calculate \sigma_b and \rho_b The Attempt at a Solution If we let the direction of polarization coincide with the z axis then...

Hey all, My year 13 physics students stumped me with this one: Why don't Neutron-Neutron (or P-P for that matter) states exist? Thanks in anticipation... Mr T

help me, please if f(X) = sin(sin(x)), use a graph to find a upper bound for abs(f(4)(x)) Thanks

What is the precise definition of the bound state condition? Thanks in advance.

Homework Statement A coaxial cable has a linear insulating material of magnetic susceptibility \chi_m separating the conductors. A current I flows down the inner conductor and returns along the outer one. Find the magnetic field in the region between the tubes. As a check, calculate the...

Homework Statement Ultrasound pulses of with a frequency of 1.000 MHz are transmitted into water, where the speed of sound is 1500m/s . The spatial length of each pulse is 12 mm. a) How many complete cycles are in each pulse? b) What is the lower bound of the range of frequencies must be...

Well, it has been ~ four years ago now I request help with this question in another thread, long dead, so I thought I would bring it to forum again in updated form: So, my question is: Does anyone know the mathematics that would explain the quantum dynamics of how a matter helium-3...

Homework Statement If electric charge did not exist, and protons and electrons were only bound together by gravitational forces to form hydrogen, derive the expressions for a_0 and E_n and compute the energy and frequency of the H_alpha line and limit of Balmer series. Homework Equations...

Okay, my homework is "Prove that there exists a positive real number x such that (x^3)=2." and I have no clue how I can solve it. sigh. Is there anyone who can me to solve it using least upper bound property?? Thank you !

Homework Statement How many bound states are there quantum mechanically ? We are told to approach the problem semi classically. Consider the Hamiltonian function H : R 2n → R (whose values are energies), and for E0 < E1 the set {(p, x) ∈ R 2n |H(p, x) ∈ [E0 , E1 ]} ⊆ R 2n ...

The current density vanishes for a bound state. I would like to know the proof and its physical significance. I appreciate the responses in advance!

Suppose a particle is subject to a spherically symmetric potential V(r) such that V(r) = -V_0, V_0 > 0, for 0\leq r \leq a and V(r) = 0 elsewhere. If we were considering a non-relativistic particle, we would have bound states for -V_0 < E < 0 (which I understand); however, since the particle is...

The base of a solid is the region bounded by y= 2*sqrt(sin(x)) and the x-axis, with x an element of [0, (pi/2)]. Find the volume of the solid, given that the cross sections perpendicular to the x-axis are squares. Work Shown: cross sections are squares: therefore A(x) is not equal to...

the asymptotic lower bound for sorting n elements is n*log(n). what about sorting a set of n elements when you know that they only take on k distinct values? does n*log(k) sound right?

If I look at the energy of the hydrogen atom, the energy is proportional to the mass of the electron (or more precisely, the reduced mass). Does this mean that without a Higgs mechanism, there are no bound states of the hydrogen atom? (Or is it just an artifact of a non-relativistic theory that...

i am given with a series called An and series Bn which from a certain place has the same members as An? prove or disprove that every partial bound of bn is also a partial bound of An ?? i know that if a series is converges then lim inf An=lim sup An is that helps? how to prove...

Homework Statement A conducting wire of length a and charge density lambda is embedded inside a dielectric cylinder of radius b. To Show: a) Bound charge on the outer surface is equal in magnitude to the bound charge inside the surface. b) volume density of bound charge is 0 in the...

I am reading an electrodynamics book to grasp the concept of bound and free charge, esp in conductor and dielectric. I got lost with the text on the book. Can anyone please help me understand the concept well?

Homework Statement Prove that the supremum is the least upper bound Homework Equations The Attempt at a Solution Proof: let x be an upper bound of a set S then x>=supS (by definition). If there exists an upper bound y and y<=SupS then y is not an upper bound (contradiction)...

Homework Statement A particle that can move in one dimension and that is in a stationary state, is bound by a potential V(x) = (1/2)kx^2. The wave function is \Psi(x,t) = \psi(x)exp(-iEt/\hbar) We look at a state in which \psi(x) = Aexp(-x^2/2a^2a^2), where a is a constant and A is the...

Homework Statement show that Ak will satisfy: \left| A_{k} \right| \leq Mk^{-4} Homework Equations A_{k} = \frac{2}{L}\int^{L}_{0} \phi(x) sin \left( \frac{k \pi x}{L} \right) dx given \phi(x) \in C^{4} ([0,L]) \and\ \phi^{(p)}(0) = \phi^{(p)}(L) = 0, p = 0, 1, 2, 3...

Homework Statement i have a finite square well and I have to calculate how many bound states exist in it. I have the depth and the width of the well but I cannot find an equation anywhere to help me calculate it?

Homework Statement I have to show that the delta function bound state energies can be derived from the finite square well potential. Homework Equations The wave functions in the three regions for the finite square well. (See wikipedia) The Attempt at a Solution 1. I start from the...

Say I have a capacitor filled with a linear dielectric in a purely electrostatic setup. Then there will exist a uniform electric field inside the capacitor, and the field inside the electrodes is of course zero. The dielectric will polarize, and I should get bound charge at the...

In all the possible potentials I have encountered so far, it seems that the bound states (i.e. E < [V(-infinity) and V(infinity)]) always results in a discrete spectrum of energies, whereas the scattering states (E > [V(-infinity) and V(infinity)]) always results in a continuous spectrum of...