Bound Definition and 501 Threads

Homework Statement Ultrasound pulses of with a frequency of 1.000 MHz are transmitted into water, where the speed of sound is 1500m/s . The spatial length of each pulse is 12 mm. a) How many complete cycles are in each pulse? b) What is the lower bound of the range of frequencies must be...

Well, it has been ~ four years ago now I request help with this question in another thread, long dead, so I thought I would bring it to forum again in updated form: So, my question is: Does anyone know the mathematics that would explain the quantum dynamics of how a matter helium-3...

I have 2 questions that need to be solve: 01. Find upper and lower bound for the k-th eigenvalue \lambda_{k} of the problem ((1+x^2)u')'-xu+\lambda(1+x^2)u for 0< x< 1 with boundary conditions u(0)=0 and u(1)=0 02. Find a lower bound for the lowest eigenvalue of the problem...

Homework Statement If electric charge did not exist, and protons and electrons were only bound together by gravitational forces to form hydrogen, derive the expressions for a_0 and E_n and compute the energy and frequency of the H_alpha line and limit of Balmer series. Homework Equations...

Okay, my homework is "Prove that there exists a positive real number x such that (x^3)=2." and I have no clue how I can solve it. sigh. Is there anyone who can me to solve it using least upper bound property?? Thank you !

Homework Statement How many bound states are there quantum mechanically ? We are told to approach the problem semi classically. Consider the Hamiltonian function H : R 2n → R (whose values are energies), and for E0 < E1 the set {(p, x) ∈ R 2n |H(p, x) ∈ [E0 , E1 ]} ⊆ R 2n ...

The current density vanishes for a bound state. I would like to know the proof and its physical significance. I appreciate the responses in advance!

Suppose a particle is subject to a spherically symmetric potential V(r) such that V(r) = -V_0, V_0 > 0, for 0\leq r \leq a and V(r) = 0 elsewhere. If we were considering a non-relativistic particle, we would have bound states for -V_0 < E < 0 (which I understand); however, since the particle is...

The base of a solid is the region bounded by y= 2*sqrt(sin(x)) and the x-axis, with x an element of [0, (pi/2)]. Find the volume of the solid, given that the cross sections perpendicular to the x-axis are squares. Work Shown: cross sections are squares: therefore A(x) is not equal to...

the asymptotic lower bound for sorting n elements is n*log(n). what about sorting a set of n elements when you know that they only take on k distinct values? does n*log(k) sound right?

If I look at the energy of the hydrogen atom, the energy is proportional to the mass of the electron (or more precisely, the reduced mass). Does this mean that without a Higgs mechanism, there are no bound states of the hydrogen atom? (Or is it just an artifact of a non-relativistic theory that...

i am given with a series called An and series Bn which from a certain place has the same members as An? prove or disprove that every partial bound of bn is also a partial bound of An ?? i know that if a series is converges then lim inf An=lim sup An is that helps? how to prove...

# bound states in a given system?? Homework Statement An electron is confined to a potential well of finite depth and width, 10^-9 cm. The eigenstate of highest energy of this system corresponds to the value ¥=3.2. a) How many bound states does the system have? b) Estimate the energy...

Homework Statement A conducting wire of length a and charge density lambda is embedded inside a dielectric cylinder of radius b. To Show: a) Bound charge on the outer surface is equal in magnitude to the bound charge inside the surface. b) volume density of bound charge is 0 in the...

I am reading an electrodynamics book to grasp the concept of bound and free charge, esp in conductor and dielectric. I got lost with the text on the book. Can anyone please help me understand the concept well?

Homework Statement Prove that the supremum is the least upper bound Homework Equations The Attempt at a Solution Proof: let x be an upper bound of a set S then x>=supS (by definition). If there exists an upper bound y and y<=SupS then y is not an upper bound (contradiction)...

Homework Statement A particle that can move in one dimension and that is in a stationary state, is bound by a potential V(x) = (1/2)kx^2. The wave function is \Psi(x,t) = \psi(x)exp(-iEt/\hbar) We look at a state in which \psi(x) = Aexp(-x^2/2a^2a^2), where a is a constant and A is the...

Homework Statement show that Ak will satisfy: \left| A_{k} \right| \leq Mk^{-4} Homework Equations A_{k} = \frac{2}{L}\int^{L}_{0} \phi(x) sin \left( \frac{k \pi x}{L} \right) dx given \phi(x) \in C^{4} ([0,L]) \and\ \phi^{(p)}(0) = \phi^{(p)}(L) = 0, p = 0, 1, 2, 3...

Homework Statement i have a finite square well and I have to calculate how many bound states exist in it. I have the depth and the width of the well but I cannot find an equation anywhere to help me calculate it?

Homework Statement I have to show that the delta function bound state energies can be derived from the finite square well potential. Homework Equations The wave functions in the three regions for the finite square well. (See wikipedia) The Attempt at a Solution 1. I start from the...

Say I have a capacitor filled with a linear dielectric in a purely electrostatic setup. Then there will exist a uniform electric field inside the capacitor, and the field inside the electrodes is of course zero. The dielectric will polarize, and I should get bound charge at the...

In all the possible potentials I have encountered so far, it seems that the bound states (i.e. E < [V(-infinity) and V(infinity)]) always results in a discrete spectrum of energies, whereas the scattering states (E > [V(-infinity) and V(infinity)]) always results in a continuous spectrum of...

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

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 & p(max)^2 = (u(not)a^{2}/4), u(not) =...

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?