Bound Definition and 476 Threads

I change the link. http://i359.photobucket.com/albums/oo31/tanzl/JavaPrinting-2.jpg Thanks SNOOTCHIEBOOCHEE

Possible bound states of a one-dimensional square well... I'm Lost! Homework Statement Find the solutions of even and odd parity from the transcendental equations then find the number of bound states that are possible for a potential such that p(max) = 4? Homework Equations p=ka/2 &...

We have a potential that is (1/2)kx^2 for x>0 and is infinity for x<0 ( half harmonic oscillator. Now i want to calculate the bound states of the system for given E. My question is this: Do we apply 1. \int p(x) dx = (n - \frac{1}{4} ) h ( Since there is only one turning point that can...

Homework Statement Find subsets E\subsetS1\subsetS2\subsetS3\subsetQ such that E has a least upper bound in S1, but does not have any least upper bound in S2, yet does have a least upper bound in S3. Homework Equations The Attempt at a Solution I got totally stuck with it. If...

Hello all. I’m researching rotational motion with a nearly harmonic potential using the basis of the particle on a ring eigenstates e(n*i*theta) defined from theta=0 to theta=2*pi. The total systems wave functions (eigenfunctions of the full Hamiltonian (KE+PE)) are then linear combinations of...

is there a relation between the density of a sphere spinning at a given rate and the degree by which the minor axis shrinks? if there is a relation, what is it. thanks a lot

Suppose I have Schroedinger equation in the form: -u''(x)+V(x)u(x)=Eu(x) The potential is such that as |x| -> Infinity, V(x) reaches a constant positive value. In this case can we have bound state/plane wave solutions for u(x) with E > 0 ?

Homework Statement Consider a permanently polarized dielectric cube with the origin of the coordinates at the center of the cube. The cube has a side of length a. The permanent polarization of the dielectric is \vec{P} = c \vec{r}. The vector \vec{r} is the radius vector from the origin of the...

Homework Statement Find the bound state energy for a particle in a Dirac delta function potential. Homework Equations \newcommand{\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } } - \frac{\hbar^2}{2 m} \ \pd{\psi}{x}{2} - \alpha \delta (x) \psi (x) = E\psi (x) where \alpha >...

Hi folks, I have a function f(t), and I want to find 2nd order polynomials that lower/upper bound f(t) in a fixed interval. For instance, f(t) = exp(2t), 0.1<t<0.4 Find a,b,c so that g(t) = a + b t +c t^2 <f(t) for the given interval I have been googling for the solution, but...

Hi all. I was thinking of something: Bound charges in an insulator arise because of the polarisation, so even though we have bound surface and volume charges, an insulator will still be electrically neutral. I was trying to apply this line of though to a magnetized object. Here, the...

Hello: There is a well known theorem which asserts that every attractive 1D potential has at least one bound state; in addition, this theorem does not hold for the 2D or 3D cases. I've been looking for a proof in my textbooks on qm but I've been unable to find it. Can you help me out? Thanks!

Does anyone know of any analytical expression for the upper bound on the Kullback–Leibler divergence for a discrete random variable? What I am looking for is the bound expressed as 0 <= S_KL <= f(k) Where k is the number of distinguishable outcomes. Ultimately I am also looking for...

Here are some papers on the covariant entropy bound conjectured by Raphael Bousso http://arxiv.org/abs/hep-th/9905177 http://arxiv.org/abs/hep-th/9908070 http://arxiv.org/abs/hep-th/0305149 It would be a significant development if the conjectured bound could be proven to hold in LQC...

if i have a quantum well structure... and i am using infinite well approximations, how do i get the maximum number of bound states supported inside each well thnks

Hi! I'd like to ask you what do the texts mean by scattering, bound and antibound states. The context for these concepts is scattering theory. Thanks!

An isolated, spherical cloud of ionized hydrogen at temperature T initially nears gravitational-electromagnetic equilibrium. How will the cloud's structure evolve?

So I'm reading "Three Roads to Quantum Gravity" by Lee Smolin, and at one point he brings up something called the Beckenstein Bound which is confusing the heck out of me. The way Smolin basically describes this (this is a popular, not a technical book, so maybe he left out some details...)...

Let Euler's zeta function be given by \sum_{n=1}^{\infty}1/n^s Is there an exponent L which limits the finiteness of (\sum_{n=1}^{\infty}1/n^s)^L for the case where s=1?

I am confused about the concept of "least upper bound". Is this line the limt of the {an} sequence. If so, how can we prove it?

1. Let A be a nonempty set of real numbers which is bounded below. Let -A be the set of numbers -x , where x \in A . Prove that \inf(A) = -\sup(-A) . Intuitively this makes sense if you draw it on a number line. But I am not sure how to formally prove it.

Let E be a nonempty subset of an ordered set; suppose \alpha is a lower bound of E and \beta is an upper bound of E . Prove that \alpha \leq \beta . So do I just use the following definition: Suppse S is an ordered set, and E \subset S . If there exists a \beta \in S such that...

Give an example of a function f for which \exists s \epsilon R P(s) ^ Q(s) ^ U(s) P(s) is \forall x \epsilon R f(x) >= s Q(s) is \forall t \epsilon R ( P(t) => s >= t ) U(s) is \exists y\epsilon R s.t. \forall x\epsilon R (f(x) = s => x = y) So this was actually a two part question, and...

Let \left\{x_{n}\right\} be a nonempty sequence of monotonically increasing rational numbers bounded from above. Prove that \left\{x_{n}\right\} has a least upper bound in \mathbb{R}. If we choose a monotonically decreasing sequence of upper bounds \left\{b_{n}\right\} with the property that...

Homework Statement Find the volume of an ice cream cone bounded by the sphere x^2+y^2+z^2=1 and the cone z=sqrt(x^2+y^2-1) Homework Equations The two simultaneous equations yield x^2+y^2=1 The Attempt at a Solution Attached

Dear All, I am searching for an upper bound of exponential function (or sum of experiential functions): 1) \exp(x)\leq f(x) or: 2) \sum_{i=1}^n \exp(x_i) \leq f(x_1,\cdots,x_n, n) . Since exponential function is convex, it is not possible to use Jenssen's inequality to get an upper bound...

Can anyone please refer to a link where Compton Scattering is treated considering the electron to be bound in the atom?

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...