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. E

    Bound States in Quantum Mechanics: Confused?

    Homework Statement I am confused about bound states in QM. My book defines bound states as those in which the particle cannot escape to infinite. It then gives an example of a potential which is infinite when x is less than 0, -V_0 when x is between 0 and a, and 0 when x >= a. But then...
  2. E

    How do I calculate the radius of bound states for muonic hydrogen?

    Homework Statement Hi I'm having difficulty in understanding how to calculate the radius for certain situations. for example, I have a question that asks me to calculate the radius and binding energy of muonic hydrogen. Homework Equations The Attempt at a Solution my first...
  3. S

    Understanding Bound States in Quantum Mechanics

    I have a question about bound states as they relate to a question on my homework... From what I can see, bound states in quantum mechanics are associated with energies that are discrete, not continuous. I don't really understand why... In my homework problem we are given a set of potential...
  4. N

    Volume Bound By Multiple Solids

    Hi, I have a question regarding appropriate methods of finding volumes bound by geometric solids. I can work through the math in MatLab by finding points in common within each solid volume...but it is very laborious and I thought that I'd ask you math people how you would tackle this...
  5. S

    Real Analysis- least upper bound and convergence

    I'm having a little difficulty understanding Epsilon in the definition of convergence. From what the book says it is any small real number greater than zero (as small as you can imagine?). Also, since I don't quite grasp what this epsilon is and how it helps define convergence, I am having...
  6. I

    What is the Dedekind section definition of a lower bound?

    in my book this is called the lower bound but it implies that it might be called the greatest lower bound elsewhere. lower bound: some quantity m such that no member of a set is less than m but there is always one less than m + \epsilon definition using Dedekind section there are quantities a...
  7. E

    Equation for a bound energy state

    Homework Statement Let V(x) = -aV_0\delta(x) Show that it admits a bound energy state of E = -ma^2V_0^2/2\hbar^2 Hint 1: Solve Schrodinger's equation outside the potential E>0, and keep the solution that has the right behavior at infinity and is continuous at x = 0. Homework...
  8. P

    Locality/nonlocality for bound states - a question

    A recent preprint on Time in Quantum Theory ( http://www.rzuser.uni-heidelberg.de/~as3/TimeInQT.pdf ) by Dieter H Zeh has brought my attention to the question of the `speed of quantum changes'. While the classical discussions of nonlocality in Quantum Mechanics (QM) and consequences of Bell's...
  9. wolram

    Can the distance between two bodies be calculated to prove they are gravitationally bound?

    Can the distance between two bodies be calculated to prove they are gravitationally bound? Use two bodies with known mass.
  10. T

    Finding Upper and Lower Bounds for Speed in km/h

    Homework Statement Martin won the 400 metre race in a time of 1 minute The time was correct to a tenth of a second The distance was correct to 1cm Find the upper and lower bounds of Martin's speed in km/h Homework Equations Speed = distance over time The Attempt at a Solution...
  11. M

    Greatest Lower Bound: Prove It!

    please i need your help! prove: "A nonempty set of real numbers bounded from below has a greatest lower bound."
  12. S

    Finding Lower Bounds for Integrals: Exploring Simple Functions

    Looking for some positive valued simple functions which are less than (or equal to) the following two integrals (given in the following post).By simple I mean that they may not involve integrals or imaginary components or some infinite series. Again, the functions may not be as simple as f(x)...
  13. A

    Bound Charges Due to Polarization

    Homework Statement We have a long cylindrical, dielectric shell in the z-axis with inner radius R1 and outer radius R2. The polarization is given by P=k/s^2 (in cylindrical coordinates, it is only in the shat direction, i.e. no zhat or phihat) Homework Equations Find the bound surface...
  14. A

    Does the expansion of spacetime affect gravitationally bound object?

    Quick question on cosmology. As everyone knows, the expansion of spacetime increases the distance between galaxies. However, I'm wondering if the same expansion increases the distance between stars in any specific galaxy. I vaguely remember my cosmology professor saying that this does not...
  15. W

    Understanding the Impossibility of a Bound State of Two Identical Nucleons

    Hello, Can someone explain to me exactly why a bound state of two identical nucleons is not possible? I have a feeling its something to do with antisymmetric wavefunction, but haven't found a satisfactory explanation in any book. Cheers.
  16. G

    All are bound to celebrate the year while Saddam faces death

    The high point of the year is drawing near, that is, it's end, however, it's pretty interesting that today's date may also coincide with Saddam's hanging; whether it was supposed to provide meaning to the event or the date was chosen to de-emphasize his death...probably both. Most individuals...
  17. P

    Applying Chernoff bound on normal distribution

    Dear all, I am trying to find out a good bound on the deveation of a normal distributed variable from its mean. The noramly distributed variables X_t \sim N(\mu, \sigma^2), t= 1,2,...,n are iid. Applying the Chebyshev inequality on the mean of these n iid variables: m_n = \frac{1}{n}...
  18. S

    Bound states for a Spherically Symmetric Schrodinger equation

    Homework Statement A particle of mass m moves in three dimensions in a potential energy field V(r) = -V0 r< R 0 if r> R where r is the distance from the origin. Its eigenfunctions psi(r) are governed by \frac{\hbar^2}{2m} \nabla^2 \psi + V(r) \psi = E \psi ALL in spherical coords...
  19. C

    Finding a Lower Bound on $\Sigma$ Function w/Green(1964)

    I was trying to find a non-trivial lower bound on the busy beaver (\Sigma) function, but I haven't been able to find the function I want. A result of Green (1964, see below) appears to have what I want, but I've never seen the actual function -- all references I have just mention the value for...
  20. EnumaElish

    Does the upper bound of computability hold for quantum computers?

    This paper states that: This means that the upper bound of computability is "10^{120} ops on 10^{90} bits." Question: does this upper bound apply to quantum computers as well?
  21. J

    Calculate an error bound of this interpolation value

    I attached the file. I am up to 1(c). Would the error bound of the interpolation value just be taylor series error term? Thanks
  22. A

    Schools College Bound -Need advice on Chemistry (Semi long)

    College Bound --Need advice on Chemistry (Semi long) This is my first post on "physics forums" so let me preface my question by saying I have been reading this forum for several weeks, and I would just like to comment on some truly exemplary people answering questions. There are some brilliant...
  23. N

    Upper Bound Theorem: Verifying Inequality & Non-Planarity

    The converse of the Upper Bound Theorem would state that a graph which satisfies the inequality e \leq { \frac{n (v-2)}{n-2} is planar. This converse is not true as seen in picture. Verify that the inequality e \leq { \frac{n (v-2)}{n-2} is true for this graph. Using the...
  24. jimmy p

    Gibraltar Bound: I'm Back & Ready for Adventures!

    I'm back! Been on holiday but now I'm back. Went to Gibraltar to see my family. Now going to move out there by September the latest. Looks like I missed a lot seeing as there are millions of threads. Is tribdog back from wherever yet?
  25. benorin

    Help showing bound for magnitude of complex log fcn

    I'm working through an example problem wherein this bound is used: \left| \log \left( 1-\frac{1}{L^s}\right) \right| \leq L^{-\sigma}, where s:=\sigma +it and it is known that \sigma >1. How do I prove this? Should I assume the principle brach is taken?
  26. W

    Learning About Bound Polarons: Definition & Development

    I want to learn the definition and development of the bound polaron. Who can help me? Thank you very much!:smile:
  27. R

    Light bending around neutron and bound photon

    I assume that the neutron is a particle with finite size and is <really> a single particle (that is that it does not have any further structure or components-like nucleus) and lastly it is electric nutral. I hope that these assumptions are close to the experimental observations. I am making life...
  28. R

    QFT & Bound States: Is Calculation Possible?

    I read somewhere that quantum field theory does not allow calculations and predictions of bound states in a satisfactory way. Is that true and how much is that a problem given that qft claims to be so fundamental?
  29. P

    Proving c+1 is an Upper Bound of S with Completeness Axiom

    Let S = \{x | x \in \mathbb{R}, x \ge 0, x^2 < c\} Show that c + 1 is an upper bound for S and therefore, by the Completeness Axiom, S has a least upper bound that we denote by b. Pretty much the only tools I've got are the Field Axioms. I think I'm supposed to do something like: x2 \ge 0...
  30. T

    How can I bound the given expression from above as x and y go to infinity?

    Hi all, we've been doing multi-variable functions and one exercise involves (or at least in the way I've been solving it) the need to bound the following from above (x and y go to infinity): \left| \frac{x+y}{x^2 - xy + y^2}\right| What I have done so far: \left| \frac{x+y}{x^2 - xy +...
  31. P

    Upper Bound for Optimal Value in Max Problem

    Obtain an upper bound for the optimal value in the following problem; Max (4x_1 + x_2 + 2x_3 + 3x_4 ) 2x_1 - x_2 + x_3 - 2x_4 <= 2 7x_1 + x_2 + 5x_3 + 10x_4 <= 4 2x_1 + 3x_2 - x_3 - x_4 <= 2 x_i >= 0 , i= 1,2,3,4 any hint.help. please. thanks note: >= means > or equal to <= means <...
  32. C

    PDE: If u is a solution to a certain bound problem, question about laplacian u

    Why does the laplacian of u=0 when u is a solution to a certain boundary problem? Is this always the case?
  33. B

    Solving Taylor Series Problem with m-th Derivative Bound

    Hi , I have some difficulties to solve this problem. It is from my numerical methods class but the problem is about taylor series: It is known that for 4 < x < 6, the absolute value of the m-th derivative of a certain function f(x) is bounded by m times the absolute value of the quadratic...
  34. P

    What is the upper bound for the given function f(t,p)?

    Dear members, I try to find the upper bound of the following function. Can anybody gives a hint? Thanks! f(t,p)=\sum_p \frac{p(1-p)}{t^5}[p^4(9t^4-81t^3+225t^2-274t+120)+p^3(-12t^4+129t^3-400t^2+524t-240)+ \mbox{\hspace{2cm}}p^2(4t^4-59t^3+...
  35. S

    Greatest Lower Bound of A - Proving it with an Axiom

    hello all I know this might be a simple question to ask, but i want to find other ways of proving it anyway here we go propve that if A is a subset of R and is non empty and bounded below, then it has a greatest lower bound. This is how i did it: let b be a lower bound of A. then for...
  36. H

    Electrodynamics: Understanding Bound Charges

    what is basically the concept of bound charges in electrodynamics??
  37. Loren Booda

    Maximum count for mutually bound stars

    Especially in the early universe, what do you think would be the maximum number of stars bound in a system under mutual attraction?
  38. B

    Bound states for sech-squared potential

    Hi, I'm working on an introductory qm project, hope somebody has the time to help me (despite the length of this post), it will be highly appreciated. My goal is to determine the bound states and their energies for the potential V_j(x) =...
  39. L

    Finding Upper and Lower Bounds for Subsets in R and Q

    For the subset M in R (real numbers) If M={1+1/n : n is an element on N) then, - All upper bounds are {x:x an element of R and x > 1} - Least upper bound is 1 - All lower bounds are {x:x an element of R and x < 0} - Greatest lower bound is 0 I am not sure if I have the above...
  40. Integral

    Just back from a short walk, for you snow bound east coasters

    This is Marys Peak, about 20mi west, and the highest point in the Oregon Coast Range http://home.comcast.net/~rossgr1/Maryspeak.jpg My front yard, it ought to be a lot better in a day or 2 http://home.comcast.net/~rossgr1/Magnolia.jpg The rest are just in the neighborhood...
  41. marlon

    What Is the New Chemical Bond Discovered Through Computer Simulation?

    https://www.physicsforums.com/journal.php?s=&journalid=13790&action=view Read the exctract in my journal and look at the site of the beautiful woman that discovered this bound with computer simulation... marlon
  42. L

    Proving Convergence of a Sequence with Upper Bound of 2

    Hey guys, I have a sequence, \sqrt{2}, \sqrt{2 \sqrt{2}}, \sqrt{2 \sqrt{2 \sqrt{2}}}, ... Basically, the sequence is defined as x1 = root 2 x(n+1) = root (2 * xn). I need to show that this sequence converges and find the limit. I proved by induction that this sequence increases...
  43. R

    Exploring Bound States in a Finite Spherical Well

    To my understanding, when a particle is in a bound state, it is "stuck" because its total energy is less than the surrounding potential. I am confused on how to prove a particular potential has no bound states. For example, in one problem, I am asked to show that there is no bound state in a...
  44. H

    Interchanging integration bound for double integral

    How do I interchange the integration bound for the function below (change to dx dy): Integral from 1/2 to 1, integral from x^3 to x [f(x,y)] dy dx ?
  45. K

    Max, min, least upper, and greatest lower bound for sets question

    Hi, I was wondering if I am doing this correctly. The question asks to state the maximum value, minimum value, least upper bound, and greatest lower bound of a bunch of given sets. The question I am asking for is this one. {x : x E (0, 1)} I am a bit confused. Therefore, is the...
  46. Loren Booda

    Inverse wavefunction incorporates lower Planck gravitational bound

    The wavefunction for a hypothetical quantum box of size Planck length (L), when inverted through L, models the universe with this lower bound required by quantum gravitational constraints. The initial quantum box solutions are given by: \phi_n=\sqrt(2/L)\\sin(n \pi x/L) However...
  47. G

    What happens to a bound electron when

    What happens to a bound electron when a photon comes along but doesn't have quite enough energy to make it go up a level? What happens to the photon? Quantum mechanical and simple answers welcome.
  48. H

    Scattered states and bound states ?

    Hello,I'm physics student.I'm from Vietnam and my English is not very good. I was wondering if anyone could help me out with a question : what are scattered states and bound states ? I'm interested in "Temperature-dependent Coulomb interation in hydrogenic systems". In this...
  49. Oxymoron

    How Can I Prove the Convergence of a Fraction with Large Exponents?

    I need some help with a question. Q) Prove that (2n^4 + 4n^2 + 3n - 5)/(n^4 - n^3 + 2n^2 - 80) converges to 2 as n goes to infinity. A) By the algebra of limits, this converges to 2 since lim(n->oo)[2 + 4/n^2 + 3/n^3 - 5/n^4]/lim(n->oo)[1 - 1/n + 2/n^2 - 80/n^4) (2 + 0 + 0 + 0)/(1...
  50. Y

    What makes a trajectory (orbit) bound?

    What makes a trajectory (orbit) bound?
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