Bound Definition and 476 Threads

  1. B

    MHB An approximated lower bound of an expression.

    Hii All, $ \sum_{i=1}^{x}i^{N}:N>2 $. Is there any approximated lower bound for the above summation? Is it > $ \frac{1}{N+1}x^{(N+1)}$ ? If yes, how to prove that?regards, Bincy
  2. M

    How to Estimate the Operator Norm ||A||_2 for a Difference Operator?

    Greetings everyone! I have a set of tasks I need to solve using using operator norms, inner product... and have some problems with the task in the attachment. I would really appreciate your help and advice. This is what I have been thinking about so far: I have to calculate a non trivial upper...
  3. H

    Excitons: Opposite Movements of Bound Electron-Hole Pairs

    How a bound electron-hole pair (exciton) can move together while the velocity of the free electron in the conduction band is opposite to that of the corresponding hole in the valence band?
  4. Saitama

    Variable Magnetic field bound in a cylindrical region

    Homework Statement There is a uniform but variable magnetic field ##\vec{B}=(B_0 t)(-\hat{k})##, in a cylindrical region, whose boundary is described by ##x^2+y^2=a^2##. ##\displaystyle \int_P^{Q} \vec{E} \cdot \vec{dy}## is (see attachment 1) A)0 B)##\frac{\pi}{4}(B_0 a^2)##...
  5. 7

    Energies and numbers of bound states in finite potential well

    Hello I understand how to approach finite potential well. However i am disturbed by equation which describes number of states ##N## for a finite potential well (##d## is a width of a well and ##W_p## is potential): $$ N \approx \dfrac{\sqrt{2m W_p}d}{\hbar \pi} $$ I am sure it has something to...
  6. A

    Brownian Particle bound by a Spring / internal Energy

    Hi, i regard a Brownian Particle connectet to a Spring and there is a heat-reservoir. The distribution of the x-coordinate of the particle follows the Diffusion-Equation (Fokker-Planck-Equation): \partial_{t}P(x,t)=\frac{D}{2} \partial_{x}^{2}P(x,t)- \Gamma\partial_{x}[f(x)P(x,t)] A...
  7. M

    Lower and Upper bound proof in R

    I am getting lost in the proof in the 5th line when it says there are 10 numbers that have the same kth digit as x. Why 10? I don't understand where this number is coming from and it doesn't seem arbitrary. the rest of the proof...
  8. michael879

    What is the maximum entropy a system can have based on its energy and size?

    ok so my main question here is about the normal bekenstein bound, but I will go into why I'm asking too in case anyone has any comments on that. The way I understand the derivation of the bekenstein bound is: If you have some closed system with energy E bounded by radius R, you can derive the...
  9. H

    Help with Problem on Bekenstein Bound

    Hi Guys, I've been struggling over a problem with the Bekenstein Bound, and I wonder if someone can help, please. The Bekenstein Bound is derived from the entropy of black holes, and says that the maximum information content of a region of space is proportional the area of that region, not...
  10. O

    MHB Least upper bound - greatest lower bound duality

    Hello everyone! There's a point I didn't get in Rudin's theorem 1.11 that says: Suppose S is an ordered set with the LUB property, and B $\subset$ S, B is not empty and B is bounded below. Let L be the set of lower bounds of B. Then a = sup L exists in S, and a - inf B. In particular inf B...
  11. M

    Production of bound states of slow fermions- Peskin 5.3

    Hi all, I've been reading section 5.3 of Peskin and Schroeder, in which the authors discuss the production of a bound state of a muon-antimuon pair close to threshold in electron-positron collisions. Here \xi,\xi' are the Weyl spinors used to construct the Dirac spinors for the muon and...
  12. N

    Doubt regarding derivation of bound charges in dielectric

    In Griffiths, for deriving the bound charges for a given polarization P , the formula used is the general formula for dipoles .i.e ( equation 4.9) {Here the potential at r is calculated due to the dipole at r' ) V(r) = ∫\frac{x.P(r')}{X^2}d\tau' Here X = r - r' , and x = unit vector in...
  13. H

    Positive lower bound in the punctured rectangle

    Homework Statement Let p(x,y) be a positive polynomial of degree n ,p(x,y)=0 only at the origin.Is it possible that the quotient p(x,y)/[absolute value(x)+absval(y)]^n will have a positive lower bound in the punctured rectangle [-1,1]x[-1,1]-{(0,0)}? Homework Equations The...
  14. P

    Bound State Wavefunctions vs Non-Bound State Wavefunctions

    Bound vs "not"bound states Homework Statement Hi, I do not understand how two bound state wavefunctions differ from not bound state wavefunctions. To be more precise I m thinking about the graphical representation. [b]ons[/b2. Relevant equati The Attempt at a Solution I speculate that bound...
  15. A

    Analytic continuation to find scattering bound states

    Hello, I am trying to understand the idea of using analytic continuation to find bound states in a scattering problem. What do the poles of the reflection coefficent have to do with bound states? In a problem that my quantum professor did in class (from a previous final), we looked at the 1D...
  16. S

    What is the Lower Bound of this Sequence?

    Homework Statement Homework Equations The Attempt at a Solution This is what I have so far: x_{n+1}=\frac{x^5_n + 1}{5x_n}=1 x_{n+2}=\frac{x^5_{n+1} + 1}{5x_{n+1}}=\frac{1^5+1}{5} I think you have to do some sort of repeated substitution but I don't quite see it. Any help? Thanks.
  17. phosgene

    Minimum energy of electron bound in nucleus

    Homework Statement An electron is confined to a nucleus of radius 4 femtometres. Estimate its minimum energy. Homework Equations ΔxΔp_x=h/4\pi E^2=p^2c^2 + m^2c^4 As the electron's rest energy will be much less than it's kinetic energy, E=pc The Attempt at a Solution So I...
  18. 8

    IS it possible to have total bound current NOT equal to 0?

    I have a permanent magnetization \vec{M}=(ks)\hat{z}, k is just a const, s is the cylindrical coor. Then it turns out that the total bound current not equal to 0. i wonder is it possible? the magnetization is stored inside the shell of a cylinder of inner radius a and outer radius b. thanks in...
  19. M

    How to Prove an Upper Bound for a Set of Real Numbers?

    Homework Statement Let A be a set of real numbers. If b is the supremum (least upper bound) of the set A then whenever c<b there exist an a in A such that a>c. Homework Equations The Attempt at a Solution I considered two cases. The first one when the supremum b is attained by...
  20. T

    Understanding Free & Bound Charges: H & D Fields Explained

    My teacher's notes don't explain this. What are free and bound charges, and why are the H and D field defined like they are?
  21. R

    Index out of bound because numel(w)=11

    Hello,, I try to convert a fortran program to matlab. I want to make an absorbing boundary model. But when I run it, I keep getting an error says: ? Attempted to access w(12); index out of bounds because numel(w)=11. Error in ==> absorb_bound_coba at 45...
  22. G

    Bound states in propagator

    Why must it be true that a system that has a bound state must have its scattering amplitude have a pole in the upper half of the complex wave-number plane? For example, if the scattering amplitude as a function of the initial wave number magnitude |k| is: A=\frac{1}{|k|-iB} with B>0, then...
  23. tom.stoer

    Number of bound states and index theorems in quantum mechanics?

    Just an idea: is there an index theorem for an n-dimensional Hamiltonian H = -\triangle^{(n)} + V(x) which "counts" the bound states (H - E) \,u_E(x) = 0 i.e. eigenfunctions and eigenvalues in the discrete spectrum of H?
  24. E

    Greatest lower bound problem - Rudin POMA Ch1 Exercise 5

    Homework Statement 5. Let ##A## be a nonempty set of real numbers which is bounded below. Let ##-A## be the set of all numbers ##-x##, where ##x\in A##.Prove that $$\inf A=-\sup(-A)\text{.}$$ Homework Equations The Attempt at a Solution Does the proof below look OK? I am a bit uneasy...
  25. R

    Difference Between Bound and Free charge

    Homework Statement So I'm having a bit of trouble getting my head around this concept and was hoping someone would be able to shed some light on it. I know the definition. i.e free charge isn't bound to a nucleus whereas bound is. But physically what difference does this make. i.e are free...
  26. B

    Least upper bound of open interval.

    I am having trouble understanding how there could be a least upper bound for an open interval. If I have (a,b) and i am looking for the least upper bound X which is the number that is less than or equal to the set of Y such that Y> all the numbers in the interval (a,b) when I think about it I...
  27. D

    Clarifications on the least upper bound property and the irrational numbers

    Hello everyone. I desperately need clarifications on the least upper bound property (as the title suggests). Here's the main question: Why doesn't the set of rational numbers ℚ satisfy the least upper bound property? Every textbook/website answer I have found uses this example: Let...
  28. A

    Bound charge in linear dielectric

    How can we show that the bound charge in a homogeneous linear dielectric is proportional to the density of the free charge. I have a handful of equations but still I can't work this out.
  29. B

    Why Do We Have Different Terms for Least Upper Bound and Supremum?

    Are the least upper bound and supremum of a ordered field same thing? If so, then why do we have two different terms and why do textbooks do not use them interchangeably. That also means that greatest lower bound and infimum are also the same thing.
  30. H

    MHB How Accurate is Lagrange Interpolation for Approximating Cos(0.75)?

    [FONT=Cambria]Problem: [FONT=Cambria]Use the Lagrange interpolating polynomial of degree three or less and four digit chopping arithmetic to approximate [FONT=times new roman]cos(.750) using the following values. Find an error bound for the approximation. [FONT=times new roman]cos(.6980) =...
  31. STEMucator

    Upper Bound Proof of Sup(SUT)=max{sup(S), sup(T)}

    Homework Statement Prove or disapprove, for non-empty, bounded sets S and T in ℝ : sup(SUT) = max{sup(S), sup(T)} Homework Equations The least upper bound axiom of course. The Attempt at a Solution Since we know S and T are non-empty and bounded in the reals, each of them...
  32. C

    Defining an upper/lower bound in lexicographically ordered C.

    If I have a lexicographic ordering on ℂ, and I define a subset, A = \{z \in ℂ: z = a+bi; a,b \in ℝ, a<0\}. I have an upper bound, say α = 0+di. My question is does only the real part, Re(α) = 0 define the upper bound? Or does the Im(α) = d have nothing to do with bounds in general? Since it...
  33. U

    Real Analysis Least Upper Bound Question

    Homework Statement If S1, S2 are nonempty subsets of ℝ that are bounded from above, prove that l.u.b. {x+y : x \in S1, y \in S2 } = l.u.b. S1 + l.u.b. S2 Homework Equations Least Upper Bound Property The Attempt at a Solution Using the least upper bound property, let us suppose...
  34. bcrowell

    Effect of cosmological expansion on bound systems in realistic cosmologies

    This paper dates to 1998: Cooperstock, Faraoni, and Vollick, "The influence of the cosmological expansion on local systems," http://arxiv.org/abs/astro-ph/9803097v1 They show that systems such as the solar system, galaxies, and clusters of galaxies experience nonzero effects from cosmological...
  35. V

    What Happens When an Electron Enters an Infinite Square Well?

    I have a question, and I'm positive it has a really simple answer, but I can't think of it right now. In the infinite square well (the simplest bound problem), the wave functions have discrete energy values. We can have a wave function that's a linear superposition of any number of these so...
  36. M

    Definite Integration with Upper bound as another integral

    i have a similar one. f(x) = \int\frac{dt}{\sqrt{1+t^3}} on (0, g(x)) g(x) = \int(1+sin(t^2))dt on (0, cos(x)) that is, these are definite integrals on the interval from zero up to the given function. the question is to solve f'(pi/2). the correct answer is -1 but i don't understand...
  37. iVenky

    Lower Bound on Q(x) for X ~ Gaussian RV

    I think everyone knows that Q(x)= P(X>x) where X is a Gaussian Random variable. Now I was reading about it and it says that Q(x) is bounded as follows Q(x)≤ (1/2)(e-x2/2) for x≥0 and Q(x)< [1/(√(2∏)x)](e-x2/2) for x≥0 and the lower bound is Q(x)> [1/(√(2∏)x)](1-1/x2) e-x2/2 for x≥0 Can...
  38. R

    The least upper bound property and the irrationals.

    Hi Does anybody know if the irrational numbers have the least upper bound property?
  39. QuestForInsight

    MHB What is the definition of greatest/least upper bound in a partially ordered set?

    Let $a$, $b$ and $c$ be elements of a partially ordered set $P$. My book defines $c$ as the greatest upper bound of $a$ and $b$ if, for each $x \in L$, we have $x \le c$ if and only if $x \le a$ and $x \le b$. Similarly, it defines $c$ as the least upper bound of $a$ and $b$ if, for each $x \in...
  40. B

    DE: Lower Bound for radius of convergence

    Prb:(x^4+4*x^2+16)y"+4(x-1)y'+6xy=0 P=(x^4+4*x^2+16) Q=4(x-1) R=6x P=0 for - 1 - 3^(1/2)*i 1 - 3^(1/2)*i - 1 + 3^(1/2)*i 1 + 3^(1/2)*i Q=0 for 1 R=0 for 0 Do we ignore Q & R, plotting P, then find shortest distance which would equal 2?
  41. lpetrich

    Are Standard-Model particles bound states?

    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...
  42. J

    Need help finding a bound for an equation

    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.
  43. A

    Could dark matter be invisible bound states of ordinary matter or ehm, aliens?

    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...
  44. B

    Find the wave function of a particle bound in a semi-infinite square well

    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...
  45. T

    Proving Continuity of f(x,y) = y/(1+x2) Using Delta-Epsilon Bound

    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?
  46. B

    MHB Finding an Upper Bound for ln(x) in [0,1]

    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
  47. N

    Higher Bound State: Definition & Meaning

    "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
  48. N

    Is the Bound State Wave Function Always Real or Imaginary?

    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...
  49. A

    Bound charges - are they real or mathematical?

    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...
  50. A

    Understanding Bound Charges and Their Mathematical Derivation

    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...
Back
Top