Bound Definition and 501 Threads

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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

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)...

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...

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...

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.

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...

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}...

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...

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...

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?

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

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...

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...

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?

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?

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

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...

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?

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...

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 +...

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 <...

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

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...

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+...

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...

what is basically the concept of bound charges in electrodynamics??

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

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) =...

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...

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...

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

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...

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...

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 ?

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...

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...

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.

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...

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...

What makes a trajectory (orbit) bound?