What is Delta: Definition and 1000 Discussions

A river delta is a landform created by deposition of sediment that is carried by a river as the flow leaves its mouth and enters slower-moving or stagnant water. This occurs where a river enters an ocean, sea, estuary, lake, reservoir, or (more rarely) another river that cannot carry away the supplied sediment. The size and shape of a delta is controlled by the balance between watershed processes that supply sediment, and receiving basin processes that redistribute, sequester, and export that sediment. The size, geometry, and location of the receiving basin also plays an important role in delta evolution. River deltas are important in human civilization, as they are major agricultural production centers and population centers. They can provide coastline defense and can impact drinking water supply. They are also ecologically important, with different species' assemblages depending on their landscape position.

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  1. S

    Explaining the Epsilon-Delta Concept in Limits

    I'm studying limits now (for the first time) and though have understood the intuitive concept of limit, I didn't get at all the epsilon-delta concept. What is epsilon and delta? What is x-2? I didn't get anything at all. So please explain me these in detail. Thanking you in advanced...
  2. Fredrik

    Question about the delta function

    No answer in the linear algebra section, so I'll try here. ("Calculus & analysis" would probably have been more appropriate than "linear algebra"). I have a question about the delta function. Link.
  3. J

    How do I convolve delta functions in Fourier transform calculations?

    Hi everyone, I need help finding the Fourier transform of Cos(10t)sin(t) i know that i need to find the transform of cos and sin and then convolve them, but i m not sure how to convolve delta function. I would really appreciate any helps.
  4. Greg Bernhardt

    Do Sleep Machines Emit Delta Waves?

    Anyone use sleep machines? My father is asking one for xmas. Are they really just cd players or is there more to it? For example this Brookstone one I am looking at has claims of delta wave technology. Is that bunk?
  5. P

    Getting a delta function from an indefinite integral

    Hey everybody, One question that I've had for a week or so now is how the following integral can equal a Dirac delta function: \frac{1}{2\pi} \int_{-\infty}^{\infty}{dt} \:e^{i(\omega - \omega^{'})t}\: = \: \delta(\omega - \omega^{'}) A text that I was reading discusses Fourier transforms...
  6. F

    Delta function antisymmetric potential problem

    Homework Statement particle of mass m is subjected to antisymmetric delta-function potential V(x) =V'Delta(x+a)-V'Delta(x-a) where V'>0 Show that there is only one bound state, and find its energy Homework Equations Assuming free particle eqn for x<-a for particle incident from -ve...
  7. D

    Explicitly Deriving the Delta Function

    When working with Fourier transforms in Quantum mechanics you get the result that \int_{-\infty}^{\infty}e^{-ikx}e^{ik'x} = \delta(k-k') I understand conceptually why this must be true, since you are taking the Fourier transform of a plane wave with a single frequency element. I have also...
  8. S

    Derive delta potential bound states from finite square well

    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...
  9. M

    Given epsilon, find delta

    I don't know how yor format this, so: x3 + x2 +x +1 The limit of that function = 0 as x approaches -1 What's the greatest value of delta when epsilon = 0.1? This is what I tried to do: |x3 + x2 + x + 1| < 0.1 -0.1 < x3 + x2 + x + 1 < 0.1 -1.1 < x3 + x2 + x < -0.9 In my...
  10. G

    [Q]Some confusing about Dirac Delta Function

    Hi. Recently day, I tried to solve quantum mechanics problem in liboff fourth version to prepare graduate school. But what make me be confused a lot is Dirac Delta Function. One of my confusing on Dirac Delta is what i wrote below. -One of the formula describing Dira Delta...
  11. P

    Kinematic Equations: T vs Delta T vs DT

    You see the variables in the kinematic equations expressed as different things sometimes such as t, delta t, dt; or d, delta x, dx; What are all the different forms of the kinematic equations with these different variables? Do you approach certain problems with certain forms or can they all...
  12. J

    Delta Epsilon Limit Proof - f(x,y) = xy

    How does one prove: limit xy = ab x-> a y -> b using the precise definition of a limit? My attempt: |xy-ab|<ϵ for: 0<|x-a|<δ/2 0<|y-b|<δ/2 it follows that: δ/2-a <x< δ/2+a δ/2-b <y< δ/2+b then: (δ/2-a)(δ/2-n) < xy < (δ/2+a)(δ/2+b) (δ^2/4-aδ/2-bδ/2 +ab)...
  13. F

    Solve Delta Potential Well for Scattering Matrix & Prove Unitarity

    Homework Statement consider the scattering matrix for the potential 2m/hbar2 V(x) = λ/a δ(x-b) show that it has the form (2ika/(2ika-λ) , (e-2kib) λ/(2ika-λ) (e2kib) λ/(2ika-λ) , 2ika/(2ika-λ) (I've used commas just to separate terms in the matrix) prove...
  14. P

    Epsilon delta to N & M Definition

    Okay for a simple finite limit: e.g. lim (3x) = 3 x->1 in the end I say: "Therefore for every |x - 3| < delta, there exists an epsilon such that |3x-3| < epsilon" Hence I can make delta really really small and the y bounds of epsilon will constrain the limit. So let's come to...
  15. M

    Dirac Delta Function Explained: Simplified for M.S Students

    hello every body i am a new M.S student and i can't understand the Dirac delta function can anyone simply describe it to me in order to simplify it. thank you
  16. Andre

    News RTL4: Delta Commission Exaggerates Climate Threats

    Meanwhile, somewhere in a backyard in Europa, a tiny TV station, RTL4 did something not seen before. It admitted that climate issues had been greatly exagarated to pursue a political project. Obviously, The Netherlands being mostly a river delta below sea level should be very keen to keep...
  17. M

    Understanding Delta PE: Why is it Equal to -W?

    1. Why delta PE=-W? In gravitation’s case, If we look at it numerically, PE= mg (b-a), W=F (b-a), then they are the same, where does the negative sign come from? Maybe that has to do with against gravitation or not? Vba=-Wba/q has the same concept. But here is one question: What minimum work...
  18. M

    How Does the Delta Function Affect Integral Values?

    Homework Statement I want to measure this integral ( Sd(x)δ(χ-c) , where c is constant Thanks in advancE Homework Equations The Attempt at a Solution
  19. J

    Distributions and delta function

    where can I read about distributions and the delta function. esp. to solve singular integrals. I have seen that you could write 1/x = \delta (x) + P.V (1/x) and all that stuff.. where can i read about it ...
  20. O

    Trouble with dirac delta in R^2

    Find a distribution F in R^2 that satisfies (Dx) F(x,t) = t*Delta(x) It is apperantly not t*H(x) as in R. * is multiplication, D is dirac delta, H is Heavyside , (Dx) is derivation with respect to x (in the sense of distributions) Sorry for not using Latex. Indeed I am trying to...
  21. maverick280857

    Integral of a delta function from -infinity to 0 or 0 to +infinity

    Hello everyone Today in my QM class, a discussion arose on the definition of the delta function using the Heaviside step function \Theta(x) (= 0 for x < 0 and 1 for x > 0). Specifically, \Theta(x) = \int_{-\infty}^{x}\delta(t) dt which of course gives \frac{d\Theta(x)}{dx} =...
  22. C

    Exploring the Relationship between the Step Function and Dirac Delta Function

    Derivative Using Dirac Delta Function Homework Statement Let \theta(x) be the step function: \theta(x) be equivalent to 1, if x > 0 0, if x \leq 0 Show that \frac{d \theta }{dx} = \delta(x) Homework Equations In the previous portion I was able to prove x \frac{d}{dx}...
  23. maverick280857

    Delta function of a function with multiple zeros

    Hi everyone, I was wondering how to deal with delta functions of functions that have double zeros. For instance, how does one compute an integral of the form \int_{-\infty}^{\infty}dx g(x)\delta(x^2) where g(x) is a well behaved continuous everywhere function? In general how does one find...
  24. G

    Star Delta Transformation Proof

    I've come across a proof for star-delta transformation which goes like this.(Refer to the diagram for notation. Pardon me for my bad drawing skills.) In the delta, he found the effective resistance between two vertices ( say a and c, which can found easily). Then he found the effective...
  25. J

    Normalization of a delta function in curved spacetime

    Which of the following are true in curved spacetime? \int d^4 x \delta^4(x - x_0) = 1 (1) \int d^4 x \sqrt{-g} \delta^4(x - x_0) = 1 (2) I think the first one is incorrect in curved spacetime, or in general when the metric is non-constant. I would argue this by saying that the delta...
  26. B

    Dirac Delta as the limit of a Gaussian

    Show that \stackrel{lim}{\alpha \rightarrow \infty} \int^{\infty}_{-\infty}g(x)\sqrt{\frac{\alpha}{\pi}}e^{-\alpha x^2} dx = g(0) where g(x) is continuous. To use the continuity of g(x) I started from \left|g(x)-g(0)\right|<\epsilon and tried to put it in into the integral...
  27. D

    Is the Reflection Coefficient for a Delta Function Potential Always Close to 1?

    So let's say we have a particle in the delta function potential, V = - \alpha \delta(x). I calculated that the reflection coefficient (scattering state) is R = \frac{1}{1 + (2 \hbar^2 E/m\alpha^2)} Now, clearly, the term 2 \hbar^2 E/m\alpha^2 is very small, as \hbar^2 has an order of magnitude...
  28. O

    Dirac Delta Function - unfamiliar definition

    Given: f(x)=\delta(x-a) Other than the standard definitions where f(x) equals zero everywhere except at a, where it's infinity, and that: \int_{-\infty}^{\infty} g(x)\delta(x-a)\,dx=g(a) Is there some kind of other definition involving exponentials, like: \int...
  29. D

    Fourier Transform, Delta Function

    Hey everybody. I was studying Fourier transforms today, and I thought, what if you took the transform of an ordinary sine or cosine? Well, since they only have one frequency, shouldn't the transform have only one value? That is, a delta function centered at the angular frequency of the wave...
  30. A

    Understanding the Relationship Between Kronecker Delta and Dirac Delta

    Is it true that \sum_x e^{i(k-k')x} = \delta_{k-k'} , where \delta is the Kronecker delta? I've come across a similar relation for the Dirac Delta (when the sum is an integral). I do not understand why k-k' \neq 0 implies the sum is zero. Edit: In fact, I'm really confused, since it seems...
  31. N

    Dirac delta spherical potential

    Homework Statement Three-dimensional particle is placed in a Dirac delta potential: V = -aV_{0}\delta(r-a) Find energy states and eigenfunctions for the angular quantum number l = 0.[/ Homework Equations The Attempt at a Solution It's not clear to me what boundary...
  32. N

    Dirac delta spherical potential

    Three-dimensional particle is placed in a Dirac delta potential: V = -aV_{0}\delta(r-a) Find energy states and eigenfunctions for the angular quantum number l = 0.
  33. H

    Dirac delta approximation - need an outline of a simple and routine proof

    Hi, I need your help with a very standard proof, I'll be happy if you give me some detailed outline - the necessary steps I must follow with some extra clues so that I'm not lost the moment I start - and I'll hopefully finish it myself. I am disappointed that I can't proof this all by myself...
  34. J

    Is Kronecker Delta a Coordinate-Independent Identity Operator?

    Can anyone give me a coordinate-independent definition of \delta^a_b on curved manifolds? Should it be defined as \delta^a_b = g^{ac}g_{bc} where abstract index notation has been used?
  35. B

    Bound state for a Dirac delta function potential

    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 >...
  36. L

    Quantum - 1D crystal model using evenly spaced delta functions

    Homework Statement Hey, the question is about delta function potentials V(x) = -g[... del(x + 3b/2) + del(x + b/2) + del(x - b/2) ...] going on out to a large x in either direction. a) sketch the ground-state wave fn, write the form of psi(x) for -b/2 to + b/2 b) show that e^z =...
  37. M

    Contour integral with delta function

    Using Cauchy's integral theorem how could we compute \oint _{C}dz D^{r} \delta (z) z^{-m} since delta (z) is not strictly an analytic function and we have a pole of order 'm' here C is a closed contour in complex plane
  38. M

    Strange representation of Heaviside and Delta function

    in the .pdf article http://repository.dl.itc.u-tokyo.ac.jp/dspace/bitstream/2261/6027/1/jfs080104.pdf i have found the strange representation \delta (x) = -\frac{1}{2i \pi} [z^{-1}]_{z=x} and a similar formula for Heaviside function replacing 1/z by log(-z) , what is the meaning ...
  39. R

    Solved Epsilon-Delta Proof: Is it Coherent?

    [SOLVED] Epsilon Delta Proof Does this limit proof make total sense? Given : "Show that \lim_{x \rightarrow 2} x^{2} = 4." My attempt at it :0<|x^{2}-4|<\epsilon which can also be written as 0<|(x-2)(x+2)|<\epsilon. 0<|x-2|<\delta where \delta > 0. It appears that \delta = \frac...
  40. V

    When can we ignore the delta function in th Feynman rules?

    in peskin-schroeder and http://www.hep.phy.cam.ac.uk/batley/particles/handout_04.pdf" the amplitude for e^-e^+\rightarrow \mu^- \mu^+ is written using feynman rules as follows -iM=[\bar{v}(p_2)(-ie\gamma^\mu )u(p_1)] \frac{-ig_{\mu\nu}}{q^2}[\bar{u}(k_1)(-ie\gamma^\nu )v(k_2)] but what...
  41. T

    Delta potential barrier in a box

    hi,... i unfortunately couldn't find a solution to this problem although it seems like a classical textbook problem... how can i solve the (time independent) schroedingerequation for the following potential V(x) = \infty for x<=-1 V(x) = a\delta(x) for -1<x<1 V(x) = \infty for x>=1 so at x=0...
  42. M

    QM - delta function potential

    Homework Statement write the radial equation for a particle with mass m and angular momentum l=0 which is under the influence of the following potential: V(r)=-a*delta(r-R) a,R>0 write all the conditions for the solution of the problem.Homework Equations Schroedinger's equation: Hu=Eu...
  43. R

    Double delta function potential

    Homework Statement Consider the double delts-function potential V(x)=-\alpha[\delta(x+a)+\delta(x-a)] How many bound states does this possess? Find the allowed energies for \alpha=\frac{\hbar^{2}}{ma^{2}}and\alpha=\frac{\hbar^{2}}{4ma^{2}}Homework Equations The Attempt at a Solution I divided...
  44. R

    Dirac delta function proof help

    [SOLVED] Dirac delta function Homework Statement Prove that \delta(cx)=\frac{1}{|c|}\delta(x) Homework Equations The Attempt at a Solution For any function f(x), \int_{-\infty}^{\infty}f(x)\delta(cx) dx = \frac{1}{c}\int_{-\infty}^{\infty}f(t/c)\delta(t) dt where I have...
  45. K

    What is the Epsilon-Delta Definition of a Limit and How Does It Work?

    I can't get my head around the epsilon-delta definition of a limit. Unfortunately I don't have a teacher to ask (I'm teaching this to myself as a self interest) so this forum is my last resort -- google hasn't been kind to me. From what I've seen, I don't really understand how the definition...
  46. J

    Dirac delta function with complex arguments

    This is probably a silly question to some, but I've been struggling to understand how the delta function behaves when given a complex argument, that is \delta(z), z \in C. I guess the basic definition is the same that the integral over all space is 1, but I'm looking for a more detailed guide on...
  47. P

    Dirac delta function and Heaviside step function

    [SOLVED] Dirac delta function and Heaviside step function In Levine's Quantum Chemistry textbook the Heaviside step function is defined as: H(x-a)=1,x>a H(x-a)=0,x<a H(x-a)=\frac{1}{2},x=a Dirac delta function is: \delta (x-a)=dH(x-a) / dx Now, the integral: \int...
  48. B

    Fourier transform of a function such that it gives a delta function.

    [SOLVED] Fourier transform of a function such that it gives a delta function. ok say, if you Fourier transform a delta function G(x- a), the transform will give you something like ∫[-∞ ∞]G(x-a) e^ikx dx a is a constant to calculate, which gives you e^ka (transformed into k space)...
  49. G

    Nonhomogeneous ODE with Dirac delta

    Trying to solve the ODE mx''(t) + bx'(t) + kx(t) = F(t) with m measured in Kg, b in Kg/s and Kg/s^2, F(t) in Kgm/s^2 and x(t) in m with initial conditions x(0) = 0 and x'(0) = 0, i got the following Green's function G(t,t') = \frac{1}{m\omega} e^{-\omega_1(t-t')}\sinh\left[\omega(t-t')\right]...
  50. C

    Dirac Delta Function question(s)

    OK, so my basic understanding of Dirac Delta Function is that it shows the probability of finding a point at (p,q) at time t. Dirac Delta is 0 everywhere except for (p_{0},q_{0}). So my question comes Is it possible that a point enters the (p_{0},q_{0}) and stays there (for some period of...
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