Bound Definition and 501 Threads

Hi, I am about to work on the problem of trying to find a renormalization program for bound states in QFT. Any suggestions/advice on where to start would be much appreciated.

is the bound state of a particle in a one-dimensional potential energy well real or complex?

Homework Statement So I've read a lot about this but still can't figure what's going on. I understand that to find the error of approximation all we have to do is: |E(x)| = |f(x)-Tn(x)| But what about M*(xn+1/(n+1)!) What's the point of this? and why does it have to be greater than or equal...

Homework Statement In 1966 Greisen, Zatsepin and Kuzmin argued that we should not see cosmic rays (high-energy protons hitting the atmosphere from outer space) above a certain energy, due to interactions of these rays with the cosmic microwave background. (a) The universe is a blackbody at...

I was just looking through a few different solutions in Griffiths EM and I must have not realized it, but do bound and free charges both contribute to the overall electric field? For example: when dealing with a capacitor with a dielectric between it, one of the solutions wants to find the...

Homework Statement Find the upper, lower and midpoint sums for $$\displaystyle\int_{-3}^{3} (12-x^{2})dx$$ $$\rho = \Big\{-3,-1,3\Big\}$$ The Attempt at a Solution For the upper: (12-(-1)^2)(-1-(-3)) + (12-(-1))(3-(-1)) =74 For the lower: (12-(-3)^2)(-1-(-3))+(12-3)(3-(-1)) =42 For midpoint...

Hello, I'm working on a lab report and am having a bit of trouble when it comes to figuring out uncertainty. Trial 1 Acceleration: 0.93 ± 0.14 m/s^2 Trial 2 Acceleration: 0.83 ± 0.35 m/s^2 Trial 3 Acceleration: 0.93 ± 0.14 m/s^2 I have three values listed above and and wanted to find the...

Hi. Hoping for some help with the following questions - 1 - Are there any momentum eigenstates in a box ? I think the answer is no because if i solve the momentum eigenvalue equation in 1-D i get Aikx but it seems impossible to get this to meet the boundary conditions 2 - As far as I know a...

Hello! (Wave) The backward Euler method We consider a uniform partition such that $[0,T_f]$ and $[a,b]$ $h=\frac{b-a}{N_x+1}, \tau=\frac{T_f}{N_t}$ $x_i=a+ih, i=0,1, \dots, N_x+1$ $t_n=n \tau, n=0,1, \dots, N_t$ $u_t-u_{xx}=0 \\ u(t=0,x)=u_0(x) \\ u(t,a)=0 \forall t \\ u(t,b)=0 \forall t$...

Recently an interested undergrad has asked me to explain holography to her. I know I'm not the best one to do that and I don't know that much, but for now, I'm the best she can have. Poor girl! Anyway, I figured its better to start from the entropy bound and explaining that the maximum amount of...

Homework Statement Compute the volume of the solid bounded by the four surfaces x+z=1,x+z=−1,z=1−y2,z=y2−1 Homework Equations Fubini's theorem? The Attempt at a Solution I have tried to visualize this solid and define the limits; when I attempted to integrate by dxdzdy (in that order), I set...

When considering the asymptotic bounds for n lgn, for what value of a in na does n lgn satisfy O(na) and for what value does it satisfy Ω(na)? For example n lgn = O(n1.261) but n lgn = Ω(n0.797). Can someone please tell me where for what a does Ω change to O? Also how does the answer change...

Homework Statement http://postimg.org/image/vzhqi8er5/ Homework EquationsThe Attempt at a Solution I understand all the calculations here - http://www.physicspages.com/2012/10/18/coaxial-cable-with-dielectric/ I have one issue that is bugging me though - if λ charge density is distributed over...

Thermodynamics question: Why does the internal energy have a lower bound? I tried to explain it using postulates, but cannot get the connection between the postulates. Please do explain it briefly. Thank you.

Hello! (Wave) We define $\delta_{h,-,2} f(x) :=- \left( \delta_{h,-}+\frac{h}{2} \delta_{h,-}^2 \right) f(x)=\frac{1}{2h} \left( -f(x-2h)+4f(x-h)-3f(x)\right)$. Let $f \in C^3[a,b]$. Then: $$| \delta_{h,-,2} f(x)- f'(x)|\leq h^2 ||f'''||_{\infty}$$ I have tried the following...

For the error bound for taylor's theorem, for the n+1 derivative evaluated at some c which maximizes the derivative my textbook says c must be between a and x..but today my teacher said that c must be between absolute value x and negative absolute value x, which is different than I thought. An...

Homework Statement Let K and L be symmetric PSD matrices of size N*N, with all entries in [0,1]. Let i be any number in 1...N and K’, L’ be two new symmetric PSD matrices, each with only row i and column i different from K and L. I would like to obtain an upper bound of the equation below...

Homework Statement Prove that if a bound sequence ##\left\{ { X }_{ a } \right\} ## is divergent then there are two sub sequences that converge to different limits. Homework Equations None. The Attempt at a Solution Ok so I am not sure if my attempt for a solution is correct or not, but I...

Dear all --- This question raises concerns already expressed in https://www.physicsforums.com/threads/the-bekenstein-bound.671770/ but in a more specific form --- so that, hopefully, a more specific answer may be given. With the Bekenstein-bound-saturated-by-BH argument, we have that a sphere...

Hello everybody. I'm interested in some problems of bound states in external fields in QFT (especially QED). I wonder are there any lectures/books or reviews which provide modern treatment of this subject? I would like to learn more about general formalism and applications in QED (I allready...

Hello, I've read in a paper that the following binomial distribution \sum_{k=floor(N/2)+1}^N{N\choose k}\varepsilon^k(1-\varepsilon)^{N-k} can be upper bounded using Chernoff bound by e^{ floor(N/2)}\,\Phi(s_0) where \Phi(s)=\left(1-\varepsilon(1-e^s)\right)^N and...

What exactly are surface bound charge and body bound charge? Is there any difference between: 1) surface bound charge and surface charge 2) body bound charge and body charge How do we know if surface and body bound charge exist? Does polarized material always have surface and/or body bound...

Hello all, Is there any lower bound on the following Binomial distribution \sum_{k=floor(N/2)+1}^N{N\choose k}\epsilon^k(1-\epsilon)^{N-k} as N goes to infinity and where epsilon is less that or equal 10^-3? Thanks

Except the extreme case of Black Holes, all other objects in the Universe (say, Galaxies) are very far from the Bekenstein bound (BB). Any object saturating the BB tends to be BH. But we can try to saturate the BB increasing the radius of a sphere. In flat static Universe, sooner or later we...

Hello! (Wave) Consider a nonuniform partition $a=t_0< t_1< \dots < t_{\nu}=b$ and assume that if $h_n=t^{n+1}-t^n, 0 \leq n \leq N-1 $ is the changeable step, then $\min_{n} h_n > \lambda \max_{n} h_n, \lambda>0$ independent of $n$. Show a bound of the error of Euler method analogous to...

Homework Statement Apply the Central limit theorem to evaluate approximately the lower bound for the probability that the difference between the relative frequency p^ and p is less than 0.01, if n = 4500 Homework Equations This exercise do not give me the confidence interval? What function...

Take some unstable particle species, and put two of them into an exotic atom or exotic molecule, such that the two bound particles fully occupy a 1s orbital. For example, two negative muons orbiting an alpha particle, or two mesons orbiting a massive baryon. Decay of either orbiting particle...

It came to me just now that because we can always take the Fourier transform of a well-behaved function, this means we can think of any such state as a superposition of free-particle momentum eigenstates. E.g., the Hermite polynomial eigenfunctions of the harmonic oscillator. They have a...

It is not clear to me, why textbooks do not mention an upper bound for the e-foldings of the basic inflation theory. To my knowledge, in order to deal with the flatness problem, we require: \frac{Ω^{-1}(t_0)-1}{Ω^{-1}(t_i)-1} = \frac{Ω^{-1}(t_0)-1}{Ω^{-1}(t_e)-1}...

Homework Statement Homework EquationsThe Attempt at a Solution for ##r \le a## and ##l = 0##, the radial equation is $$- \frac {\hbar^{2}}{2m} \frac {d^{2}u}{dr^{2}} - V_{0} = Eu $$ $$- \frac {\hbar^{2}}{2m} \frac {d^{2}u}{dr^{2}} - [V_{0} + E]u = 0$$ call ##k^{2} = \frac...

In 1-D if I have an infinite potential at x<0 so the wavefunction is zero for x<0 but for x>0 the potential is zero so the wavefunction oscillates to infinity is that a bound state ? I presume this isn't bound as it can't be normalized but most definitions state that bound means the wavefunction...

Homework Statement [/B] The magnitude J of the current density in a certain wire with a circular cross section of radius R = 2.20 mm is given by J = (3.07 × 108)r2, with J in amperes per square meter and radial distance r in meters. What is the current through the outer section bounded by r =...

Since I'm not sure if posting assignment questions is allowed, I'm just going to ask specific questions just to be safe. 1. Homework Statement Find all the lower bounds of given pair. Say (a, b) in T. Homework Equations Proof for greatest lower bound: ∀g,a,b ∈ T ⇔ ( g ≺ a) ^ (g ≺ b) ^ (...

Homework Statement What is the closest celestial object that has bound synchronous rotation with another object? Homework Equations - The Attempt at a Solution I am almost sure it's Moon.

I have looked around for help with this, including on existing threads, but I can't quite find what I'm looking for. I know that in the nuclear shell model we fill the shells in the same way as with electrons, so 2 protons in the first and 6 in the second etc, with the same being true for...

Homework Statement I was given a task to model (using Matlab) 3 identical particles in external field and find spectra of lowest system energy states using gradient descend method for each particle in the system. I did a run of 500 random generated coordinates and found this distribution...

Homework Statement I'm curious in proving that expectation value of momentum for any bound state is zero. So the problem is how to prove this.Homework Equations $$ \langle \mathbf{p_n} \rangle \propto \int \psi^*(\mathbf{r_1}, \dots ,\mathbf{r_N}) \nabla_n \psi(\mathbf{r_1}, \dots...

Homework Statement Find the error bound using Simpsons Rule for integral of SQRT (x) dx from 1 to 9.[/B]Homework Equations E = (M * (b-a)^5) / (180 * n^4), where M = max value of the 4th deriv of x dx [/B]The Attempt at a Solution see attached please - I can't figure out what to use for the...

A magnetized object is always described as having bound volume and surface current. Are these bound currents real? I mean if I connect a galvanometer between two points on the surface of a magnetized iron sphere, will the galvanometer show a deflection? If it does then it is very strange because...

If the magnetization vector is in the z direction, is the bound surface current of a cube always 0, since z cross z is 0, and x and -x cancels and y and -y cancels out?

Homework Statement Prove if an ordered set A has the least upper bound property, then it has the greatest lower bound property. Homework Equations Definition of the least upper bound property and greatest lower bound property, set theory. The Attempt at a Solution Ok, I think that my main...

Homework Statement Show that this function has no absolute max by showing that it is unbounded Homework Equations f(x,y) = (x-1)^2 + (y+2)^2 -4 The Attempt at a Solution my initial idea is to construct a sequence of points {(xk, yk)} so that the sequence {f(xk, yk)} becomes unbounded. to...

Hi! (Wave) $$\text{ I want to prove that } n \cdot 4^n=O(n!), \text{ so that } \exists c>0, n_0 \geq 0, \text{ such that } \forall n \geq n_0: n \cdot 4^n \leq c \cdot n!$$ That's what I have tried: $$n \cdot 4^n=n \cdot \underbrace{4 \cdot 4 \cdots 4}_n=4 \cdot 4 \cdot 4 \cdot4 \cdot...

Hello! (Wave) I want to find an asymptotic upper bound for the recurrence relation: $T(n)=9T \left (\frac{n}{3} \right ) + n^2 \log n $, $T(n)=c, \text{ when } n \leq 9$, using the following method: We choose a specific function $f(n)$ and we try to show that for an appropriate $c>0$ and an...

Hi there I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as: E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2 If solved properly, it should give one curve (RHS), crossed...

1)So from my understanding, as long as ##E>0## you will have scattering states and these scattering states will always result in an imaginary ##\psi##, but bound states can also have an imaginary ##\psi##? Is this correct and or is there a better way of looking at this maybe more conceptually...

I'm working on a problem out of Griffith's Intro to QM 2nd Ed. and it's asking to find the bound states for for the potential ##V(x)=-\alpha[\delta(x+a)+\delta(x-a)]## This is what I'm doing so far: $$ \mbox{for $x\lt-a$:}\hspace{1cm}\psi=Ae^{\kappa a}\\ \mbox{for $-a\lt x\lt...

Homework Statement We learned in class that a particle exposed to a 1D delta-function potential well would always have a single bound state. Let us now explore this question for the case where the delta-function potential well is situated in the vicinity of the impenetrable potential wall...

Homework Statement Hi! Not sure if I'm posting in the right section, this problem is from a course in scientific computing. Anyway, we're considering a set of PDEs: u_t + Au_x = 0 \quad 0<x<1, \ t>0 \\ u(x,0) = f(x) \quad 0 \leq x \leq1 \\ u_1(0,t) = 0 \quad t \geq 0 \\ u_2(1,t) = 0 \quad t...

Homework Statement Hi! My issue here is that I need to find the bound states (if any) of the potential: U(r)=-C\frac{s_1\cdot \hat{r}\, s_2\cdot \hat{r}-s_1\cdot s_2}{r}. Here s_1 and s_2 are the spins of the two spin-one particles involved in this interaction. The two particles have...