Bound Definition and 501 Threads

Hi, I asked this question in the quantum physics forum https://www.physicsforums.com/showthread.php?t=406171 but (afaics) we could not figure out a proof. Let me start with a description of the problem in quantum mechanical terms and then try to translate it into a more rigorous mathematical...

Consider a uniform, isotropic , homogeneous solid dielectric slab. We know, induced surface charge=\overline{P}.\widehat{n} and \overline{P} \alpha \overline{E} So, as applied electric field increases, polarization per unit volume increases. which implies that surface...

Hi, I discussed this with some friends but we could not figure out a proof. Usually when considering bound states of the Schrödinger equation of a given potential V(x) one assumes that the wave function converges to zero for large x. One could argue that this is due to the requirement...

Hello, Up until now I was certain that a bound state is a state with energy below the minimum of the potential at infinity. However, in this question I don't know at all how to proceed. Homework Statement A spin 3/2 particle moves in a potential V=V_0(r)+\frac{V_1}{r^3}L\cdot S and V0 > 0. We...

i have two questions that i am struggling with and i have tried all i can think of with them and i am still not getting the answers correct. 1)Estimate, using the Uncertainty Principle, the kinetic energy of an electron if it were bound in the nucleus. Answer: ∼ 200 MeV for R ∼ 1 fm...

Hi guys, just got owned by my calc prof with a final exam question. Very very weird. Attempted it and different approach apparently gets u different answers. I have no idea what's going on.. I have attached the question as a word document. Too much integration to type and I cannot really use...

Hey Guys, Am working through Relativistic Quantum Mechanics: Wave equations by W.Greiner and have a simple question about the Klein-Gordon equation: is it fair to say that bound states only occur between -m<=E<=m? (c=1). There are a few problems where they show that you can get pair...

Homework Statement Let \mathcal{F} \subset C(\mathbb{R}) be a set of continuous functions such that for each x \in \mathbb{R} there is an M_x > 0 such that |f(x)| \leq M_x for all f \in \mathcal{F}. Homework Equations Prove that there is a nonempty open subset Y \subseteq X and an M...

I have read in a book about bound vectors that we can not move them i mean that they can not move parallel to any location. Can someone please give me an example. Also if we are given two bound vectors, is it possible to find the dot and cross product of two vectors.

These days I met one problem and asked a professor for help. But I can not understand his answer. Can you help me explain his answer? My question is that whether we can assume that a plane wave is orthogonal to the bound state of Hydrogen atom when t->\infty? Professor answers...

ok. this is an easy enough thing to prove in one dimension but my question seems to be 3 dimensional and it's causing me some hassle: show the expectation value of the kinetic energy in a bound state described by the spherically symmetric wavefunction \psi_T(r) may be written \langle...

Homework Statement Estimate sin4 accurate to five decimal places (using maclaurin series of sin) Homework Equations The Attempt at a Solution Lagrange error bound to estimate sin4° to five decimal places( maclaurin series) 4°=pi/45 radians |Rn(pi/45)<1*(pi/45)^n+1/(n+1)...

Hello, Well, actually it's not a homework problem, I just got really confused about bound charges. Originally, I thought it was just a special technique to do the integral, but somehow Griffiths suggest that bound charges are phsically exist.(chap. 4.2.2) Well, I can accept his argument...

Find the total mass that occupies a solid region D bounded by a sphere of radius 3 centered at the origin and z = 1 if the density of the function is (x, y, z) = 1/1+x^2+y^2+z^2 . I would like to be able to do this problem using spherical coordinates but I am unsure about how...

How does one solve bound state problems in QFT(like an electron positron atom)? How does one identify the space of states. The Fock space seems to lose it definition when a bound state problem is discussed. There is also no meaning to wave functions or potentials that are used in standard...

Homework Statement I am given the following two functions: y=x3-13x2+40x and y=-x3+13x2-40x I need to find the area bound between the above two functions. Homework Equations Integrals! The Attempt at a Solution I don't know how to do this as there is 3 points of intersection...

My question: Should the sum of all bound currents always be zero? For example, should the bound currents of a cylinder with both bound volume current density and bound surface current density always sum up to zero? Does the uniformity of current ran through the cylinder have any effect...

Homework Statement The region bounded by the given curves is rotated about x = 10 x=1-y^{4}, x=0 Find the Volume V of the resulting solid by any method. Homework Equations The Attempt at a Solution I'm using the washer method. Not sure if it is being setup properly as I'm getting the...

Say you have a Yukawa potential (a.k.a. screened coulomb potential) V(r) = -\frac{e^2}{r}e^{-rq} where q is the inverse screening length, how would you find the critical q for having bound states? I'm working on reproducing N.F. Mott's argument about the critical spacing of a lattice of...

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...

Homework Statement I am to find the particles trajectory to the first order of r/a knowing it to have the Yukawa potential v(r)=V_{\circ}r_{\circ}/r * e^{-r/r_{\circ}} = -k/r * e^{-r/a} Homework Equations \theta(r)= \int (1/r^{2})/\sqrt{2\mu (E-U-l^{2}/2\mu r^{2}}) dr...

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...