What is Bound: Definition and 501 Discussions

Outward Bound (OB) is an international network of outdoor education organizations that was founded in the United Kingdom by Lawrence Holt and Kurt Hahn in 1941. Today there are organizations, called schools, in over 35 countries which are attended by more than 150,000 people each year. Outward Bound International is a non-profit membership and licensing organisation for the international network of Outward Bound schools. The Outward Bound Trust is an educational charity established in 1946 to operate the schools in the United Kingdom. Separate organizations operate the schools in each of the other countries in which Outward Bound operates.Outward Bound helped to shape the U.S. Peace Corps and numerous other outdoor adventure programs. Its aim is to foster the personal growth and social skills of participants by using challenging expeditions in the outdoors.

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  1. .Scott

    B Crossing the Bekenstein Bound at Black Hole Event Horizon

    The Bekenstein Bound places a upper limit on the amount of entropy that a given volume of space may contain. This limit was described by Jacob Bekenstein who tied it quite closely to the Black Hole Event Horizon. Put simply, black holes hold the maximum entropy allowed for their volume. If you...
  2. R

    A Bound states of an electron trapped in a dipole field

    The problem of bound states of an electron trapped in a dipole field is being studied by Alhaidari and company. (See, for example, https://arxiv.org/ftp/arxiv/papers/0707/0707.3510.pdf). It is not clear to me why the point dipole approximation is used everywhere in such calculations. Can't an...
  3. X

    A Minimum-variance bound for the extended maximum likelihood estimation

    I am fitting a mass spectrum using pdf(M)=Ns×S(M)+Nb×B(M; a, b) to determine the yield with the extended maximum likelihood fit, where Ns and Nb are the number of signal and background events, S(M) is the function for the signal, B(M;a, b) is the function for the background with parameters a and...
  4. Harikesh_33

    I Question regarding how to interpret dipole moment for bound charges

    How do I interpret physically what dipole moment is ? The explanations that I received were "two charges seperated by a small distance " ,"it talks about ability of a dipole to rotate under the influence of an Electric Field " ,"Second term of the Multipole expansion" ,I get that these terms...
  5. lua

    Upper bound for first excited state - variational principle

    I'm solving problem number 5 from https://ocw.mit.edu/courses/8-05-quantum-physics-ii-fall-2013/resources/mit8_05f13_ps2/. (a) Here I got: $$ \beta = \frac{\hbar^{\frac{1}{3}}}{(\alpha m)^\frac{1}{6}} $$ and: $$ E = \left ( \frac{\alpha \hbar^4}{m^2} \right )^\frac{1}{3}e $$ (b) Using Scilab I...
  6. H Ucar

    A Magnetic bound state in classical mechanics

    Seven years ago, I wanted to share and discuss my experiments results there but it was not possible since there was no published peer review paper yet and apparently not fulfilling forum requirements. Now we have such a publication, but still not sure the subject can be discussed here. Anyway...
  7. warhammer

    Seeking Guidance to Find Surface & Volume Bound Charges of a Half Cone

    This was a trivial question I had (which I posted here on the PF EM Forum: https://www.physicsforums.com/threads/bound-charges-polarisation-of-a-half-cone.1015308/). As I received no response on the above link I decided to post the same as a self formulated HW problem. Below I have attached an...
  8. H

    Bound charges of a block (top and bottom surface)

    From what I think, to find the bound charges of a block on the top and bottom surface I have to find the electric field or the displacement (D). However, I'm not sure how to proceed with a cube. For example, with a sphere ##E = \frac{Q}{4\pi \epsilon_0 r^2}## since r is constant. For a cube, it...
  9. docnet

    Derive an upper bound for |f(i)|

    ##\mathbb{D}## is open. Let ##\mathbb{A}:=\{z:|z-i/2|=\frac{1}{9}\}##. ##\mathbb{A}## is closed and contained in ##\mathbb{D}##. ##f## is analytic in ##\mathbb{D}##, so ##f## is analytic on the interior to and on ##\mathbb{A}##. By the Cauchy integral formula, ##f^{(4)}## exists at every point...
  10. G

    B Grain direction for maximum tear resistance for a wire bound book

    Paper has a grain direction – the direction of the long fibres. For several reasons, publishers always print hardcover books with the grain of the paper in the same direction as the fold. I'm working on a book that will be 2:1 wire bound (two holes to the inch). I was wondering what the grain...
  11. P

    I Finding a bound for a fraction

    Hi, I have given the following, which I would like to show that this estimation is correct, where ##|\theta| \leq \frac{\pi}{^2}## and ##M \geq 1##: $$\frac{1}{M^2}\frac{\sin^2(M\theta)}{\sin^2(\theta)} \geq \frac{4}{\pi^2}$$ I would approach an estimation of the denominator via ##\sin(x)...
  12. Gustav

    Calculating Bound Charge Density & Polarization

    I have already calculated the polarisation that is $$ \mathbf{P} = \frac{\rho_f r}{2} \left( 1 - \frac{\epsilon_0}{\epsilon} \right) \hat{r} . $$ I tried to use the following formulas to calculate the density bound charges. For the surface bound charge I got: $$ \sigma_{b1} = \mathbf{P} \cdot...
  13. A

    Ohm's law, current density, free & bound charge

    Hello, I wonder if you could give me some advice to how solve this question. What I was thinking to solve it was to determine J by using Ohms law, ## \vec J = \sigma_{\alpha} \vec E ## I already determined the E field for for the sphere, I got it from a) ("a)" was to determined all the bound...
  14. Gustav

    Electrodynamics: bound charges

    I was trying to solve it using the formula for polaresation P = ε E - ε0 E. Then I tried to solve for E which is D/ε and D= ρf/ε. So at the end, I will have something as P = pf- (ε0ε). ρb = -∇ * P = 0 so σb = P * n = ...? I am unsure what the direction for the polaresation should be? I need...
  15. M

    Bound correlation coefficient for three random variables

    Hi, I just found this problem and was wondering how I might go about approaching the solution. Question: Given three random variables ## X##, ##Y##, and ## Z ## such that ##\text{corr}(X, Y) = \text{corr}(Y, Z) = \text{corr}(Z, X) = r ##, provide an upper and lower bound on ##r## Attempt: I...
  16. A

    I Index and bound shift in converting a sum into integral

    Considering the below equality (or equivalency), could someone please explain how the bounds and indices are shifted? $$\sum_{i=2}^{k}(h_i/f_{i-1})=\int_{1}^{k}(h(i)/f(i))di$$
  17. P

    I Do nucleons have a lower energy state when bound in a nucleus?

    But when I look at the definition of binding energy that doesn't make seem to make sense. It looks as though they had more energy when they were together and when they were separated that energy turned to mass (the mass defect)? Am I looking at this right? I also don't understand this...
  18. J

    A Feynman diagram for bound particle output

    I am interested on how Feynman diagram is formed from a differential equation model of particle interaction wherein the incoming particles are not bound (e.g., separated neutron, proton and electron) and one or more of the outgoing particles are bound (e.g., hydrogen atom). However, I had never...
  19. geshel

    I Holographic Principle and/or implications of the entropy bound

    Hi all, First post here. I'm a casual physics enthusiast, but I've been reading and thinking a lot about this topic lately. The thing I'm most interested in is the fact that black hole formation involves the simultaneous limits of two things: time dilation and the information bound. I find it...
  20. L

    Delta potential problem - bound states problem

    I am confused here. For ##x>0## particle is free and for ##x<0## particle is free. That I am not sure how we can have bond states. If particle is in the area ##x>0## why it feel ##\delta## - potential at ##x=0##. Besides that, I know how to solve problem. But I am confused about this. If we...
  21. L

    I Double delta potential -- Degeneracy of bound states in one dimension?

    I have a question from the youtube lecture That part starts after 42 minutes and 47 seconds. Balakrishnan said that if delta barriers are very distant (largely separated) then we have degeneracy. I do not understand how this is possible when in 1d problems there is no degeneracy for bond states.
  22. Mathman2013

    Calculating Minimum Water Level in a Barrel using ODE: Analysis and Approach

    I have following differential equation dV/dt = 5 - 2 * V(t)^(1/3) which represents a the time its take to drain a barrel of rain water which contain 25 Liter of water, at t = 0. I am suppose to calculate the least amount of water in barrel during this process. If I set the rate of growth to...
  23. C

    MHB Upper Bound of Sets and Sequences: Analyzing Logic

    Upper bound definition for sets: $ M \in \mathbb{R} $ is an upper bound of set $ A $ if $ \forall \alpha\in A. \alpha \leq M$ Upper bound definition for sequences: $ M \in \mathbb{R} $ is an upper bound of sequence $ (a_n)$ if $ \forall n \in \mathbb{N}. a_n \leq M$ Suppose we look at the...
  24. yucheng

    Prove the lower bound for a sequence (Buck, Advanced Calculus)

    Clearly, ##x_{n+1}>x_n \because x_n + \sqrt{x_n} > x_n## $$ \begin{align*} x_{n+1} &= x_n+ \sqrt{x_n} \\ &= x_1 + \sqrt{x_1} + \sqrt{x_2} + \cdots \sqrt{x_n} \\ &>n+1 \end{align*} $$ ##\because \sqrt{x_n}>\sqrt{x_1}=1## In fact, $$x_{n+1} > 1+ \sqrt{1} + \sqrt{2}+ \sqrt{3} + \cdots \sqrt{n}$$...
  25. Mayan Fung

    I Discreteness of bound vs unbound states

    I observe that all bound states have discrete energy levels, eg. particle in a box, hydrogen atoms. But unbound states always have a continuous energy spectrum. For example, for the case of a finite potential well, when ##E<V_0##, we have discrete energy for the bound states. When ##E>V_0##, the...
  26. Kostik

    A Upper bound for wavelength of a photon inside an infinite square well

    Obviously a particle inside an ISW of width L cannot have arbitrarily precise momentum because ΔP ≥ ℏ/2ΔX ≥ ℏ/2L. Therefore you cannot have a particle with arbitrarily low momentum, since that would require ΔP be arbitrarily small. I need to show that a photon inside an ISW cannot have...
  27. Mr_Allod

    Bound Bulk Current Density and Surface Current Density

    Hi there, I've worked through most of this question but I'm stuck on the final part, showing that total bulk current ##I_B## is equal and opposite to total surface current ##I_S##. I calculated ##\vec H## the normal way I would if I was looking for ##\vec B## in an infinitely long cylindrical...
  28. person123

    Why are two pieces of wood stronger when bound together?

    The answer learned in class is that the two 2*4s are able to distribute the load over both of them, but I don't think this is an actual answer because that's balanced by the fact that each block is half the area. Does anyone know of the reason for this observation? Thanks!
  29. Tony Hau

    Solve Bound Charge Question: Griffith's Book Example

    This is an example of Griffith's book on bound charge, and the following is the solution to this example. We choose the z-axis to conincide with the direction of polarization. By $$\sigma_b \equiv \mathbf P \cdot \hat {\mathbf n} $$ and $$\rho_b \equiv - \nabla \cdot \mathbf P$$ we can...
  30. P

    MHB Exploring Finite Group Theory: Finding the Upper Bound of Groups of Order

    In the context of group theory, there's a theorem that states that for a given positive integer \(n\) there exist finitely different types of groups of order \(n\). Notice that the theorem doesn´t say anything of how many groups there are, only states that such groups exist. In the proof of this...
  31. A

    A Energy needed to convert a bound proton to a neutron?

    Hey everyone, I've got a question on converting bound protons into neutrons. a. What are some methods used to achieve the proton-to-neutron conversion in atomic nuclei? I'm familiar with particle scattering off a proton in the nucleus. I'm also aware of (n,p) reactions. Are there any other...
  32. M

    Engineering Plastic Analysis: Upper Bound Theorem

    Hi, I have a quick question about part 1 of this upper bound theorem question (in the attached image). Answer says that \lambda_c = 2.25 . First, we know that there is 1 redundancy and therefore there will be a maximum of 2 plastic hinges for failure. I have found that there needs to be...
  33. F

    Upper bound height and lower bound height of a 3-ary ordered tree

    how to find upper bound height and lower bound height of 3-ary ordered tree that have leaves of 101? ( the tree don't have to be complete tree, but have to be have 3 children) $$m^h \ge 101=3^h \ge 101$$ $$log \, m^h \ge 101=3^h \ge 101$$ $$h \ge 5$$ but how to know upper bound and lower...
  34. S

    Is the Ion Bound with this Energy Minimization?

    From what we did in class, I think we need to minimize the energy with respect to a. Like ##E = \frac{\hbar ^2}{m} a^2 - 2 e^2 a + \frac{5}{8} e^2 a = \frac{\hbar ^2}{m} a^2 - \frac{11}{8} e^2 a ##, then minimize it Finding the minimum value: ## - (\frac{11}{16})^2 \frac{m e^4}{\hbar^2} ##...
  35. F

    I Is force a a bound vector or a free vector?

    Hello Everyone, A small dilemma: is force, which is a vector, a free vector, since it can be slid along its along of application, thus changing its point of application (principle of transmissibility) or a bound vector, since the point of application of the force is crucial for the effect the...
  36. S

    I "Dumb" question : is there an upper bound on the energy of a photon?

    I was wondering if anybody knew if there was an upper bound on how much energy you can pack into a photon, if such a thing exists. I'm wanting to say no there isn't but it occurred to me that I did not know the answer. Sorry if this is an absurdly easy question but I don't remember reading...
  37. Jamister

    A QED Bound States: Weinberg's Explanation & Breakdown

    Weinberg writes in his book on QFT Vol1 that bound states in QED are problematic because perturbation theory breaks down. consider the case of hydrogen atom, electron+proton. Weinberg explains this case and I copy from the book: https://www.physicsforums.com/attachments/247655 what is time...
  38. S

    Least Upper Bound Property ⇒ Archimedean Principle

    Hello! I was wondering if this proof was correct? Thanks in advance! Given: A totally ordered field, ##\mathbb{F}##. Claim: Least Upper Bound Property (l.u.b.) ⇒ Archimedean Principle (AP) --- Proof. I will show that the contrapositive is true; that is, if ##\mathbb{F}## does not have the AP...
  39. S

    Lagrange error bound inequality for Taylor series of arctan(x)

    The error ##e_{n}(y)## for ##\frac{1}{1-y}## is given by ##\frac{1}{(1-c)^{n+2}}y^{n+1}##. It follows that ##\frac{1}{1+y^2}=t_n(-y^2)+e_n(-y^2)## where ##t_n(y)## is the Taylor polynomial of ##\frac{1}{1-y}##. Taking the definite integral from 0 to ##x## on both sides yields that...
  40. jk22

    A Tsirelson bound and mixed states.

    Could it be possible that using a mixed stated ##\rho=\sum_{i=1}^4|\langle e_i|\Psi\rangle|^2|e_i\rangle\langle e_i|## Where ##\Psi## is the singlet state and the ##e_i## form an orthonormal basis (like an intermediary state),That one could violate Tsirelson's bound if the parameters describing...
  41. nmsurobert

    I Gravitationally bound galaxies

    How do we know if galaxies are gravitationally bound? I'm guessing it obviously has something to do with the mass of each galaxy in the cluster, but is there an equation that is used to determine when they are bound to each other? Is there some kind of measurement made regarding the velocity...
  42. V

    Finding an upper bound that is not the supremum

    I just want to see if I did this correctly, the interval (0,1) has 2 as an upper bound but the supremum of S is 1. So M would be equal to 2? Thank you.
  43. U

    I Proving Alternating Derivatives with Induction in Mathematical Analysis I

    Hi forum. I'm trying to prove a claim from Mathematical Analysis I - Zorich since some days, but I succeeded only in part. The complete claim is: $$\left\{\begin{matrix} f\in\mathcal{C}^{(n)}(-1,1) \\ \sup_{x\in (-1,1)}|f(x)|\leq 1 \\ |f'(0)|>\alpha _n \end{matrix}\right. \Rightarrow \exists...
  44. A

    How does the dielectric affect the charge distribution on a charged sphere?

    Homework Statement [/B]Homework Equations [/B] ∫Dperpendiculards=qenclosed freecharge D=ε0E+P The Attempt at a Solution D1+D2=q/2πr2 at a distance r from the centre How to find D2 which is at the lower boundary e.g inside the dielectric??
  45. D

    Bound surface charge on a linear dielectric half-cylinder

    Homework Statement Problem statement in attached photo. This is an ungraded assigned problem which I am using to study for an exam, so I don't need the whole solution just help with a couple of points I am confused about. One: Part d) is really important to how I will answer part b). If we can...
  46. Clara Chung

    Bound current of a magnetized object

    Why is the current of the boundary uniform?
  47. B

    Gravitationally bound and Hubble time

    Homework Statement Estimate how long a galaxy in the Coma cluster would take to travel from one side of the cluster to the other. Assume that the galaxy moves with a constant speed equal to the cluster’s radial velocity dispersion. How does this compare with the Hubble time, t H ? What can you...
  48. I

    Are electrons bound to the nucleis?

    I'm not questioning whether electrons exist or whether or not they have a role in chemical bonding. I'm just asking how we know the nucleis and electrons are just parts of a larger whole, aka the atom.
  49. A

    I Finite square well bound states

    Let's suppose I have a finite potential well: $$ V(x)= \begin{cases} \infty,\quad x<0\\ 0,\quad 0<x<a\\ V_o,\quad x>a. \end{cases} $$ I solved the time-independent Schrodinger equation for each region and after applying the continuity conditions of ##\Psi## and its derivative I ended up with...