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. J

    Transmission Coefficient of a double delta function potential

    V(x) = |g| (δ(x+L)+δ(x-L) Consider scattering from a repulsive twin-delta function potential. Calculate R and T. I'm mostly confused about computing the T coefficients for multiple barriers. Would I compute the T coefficient for the barrier at x = -L and at x = L seperately? Then...
  2. A

    Dirac delta and fourier transform

    In my book the dirac delta is described by the equation on the attached picture. This realtion is derived from the Fourier transform, but I'm not sure that I understand what it says. If u=t it is clear that one gets f(u) in the Fourier inversion theorem. But why wouldn't u=t? In the derivation...
  3. A

    Why is the Dirac delta function written as δ(x-x') instead of just δ(x')?

    What's the reason that you write δ(x-x') rather than just δ(x') both indicating that the function is infinite at x=x' and 0 everywhere else? For me that notation just confuses me, and in my opinion the other notation is easier.
  4. T

    Limit involving dirac delta distributions

    Hey All, I am trying to evaluate the limit: \lim_{x\to 0^{+}} \frac{\delta''(x)}{\delta''(x)} Where \delta'(x) is the first derivative of the dirac distribution and \delta''(x) is the second derivative of the dirac distribution. I thought about the fact that this expression...
  5. P

    Complex exponential X delta function

    1. Problem Statment: Sketch the sequence x(n)=\delta(n) + exp(j\theta)\delta(n-1) + exp(j2\theta)\delta(n-2) + ... 3. Attempt at the Solution: The angle theta is given in this case Can someone remind me of how to multiply a complex exponential by a delta function? This sequence represents...
  6. B

    Multivariable Delta Function Integral

    Homework Statement I have to find this integral: \int \delta (( \frac{p^{2}}{2m} + Cz ) - E ) p^{2} dp dz where E, m, and C can be considered to be constants. Homework Equations I'm semi-familiar with delta functions, i.e. i know that: \int \delta (x - a) dx = 1 and that you can usually...
  7. Ƒ

    Why Do We Use |x-2| < 1 and δ = min{1,ε/5} in Epsilon-Delta Proofs?

    For part A, (described here: http://www.cramster.com/solution/solution/1157440) I don't understand why they say |x-2| < 1 and why \delta = min{1,ε/5} In case you can't view the page: lim x2+2x-5 = 3, x \rightarrow 2 Let ε > 0 and L = 3. |x2 + 2x -5 -3| < ε |x2 + 2x - 8| < ε |x+4||x-2| < ε...
  8. S

    A simple application of dirac delta shift theorem help

    A "simple" application of dirac delta "shift theorem"...help Homework Statement show that for a, b, c, d positive: δ(a/b-c/d) = bdδ(ad-bc) Homework Equations ∫f(x)δ(x-a)dx = f(a) The Attempt at a Solution Ok so I start with ∫δ(a/b-c/d)f(x)dx But I am not sure how to apply the shift...
  9. P

    What is Delta Δ? Uses & Meaning

    What is delta ##Δ##, where and why do we use it ?
  10. H

    A real challenge: real gas isothermal delta h

    Homework Statement Using any software, create the enthalpy table for the following two cases of superheated steam: 1. Isobaric process at a chosen pressure in 100 spaces of 5 degrees celcius. 2. Isothermal process at a chosen temperature, given Vg from the book, in 1000 spaces of 0.1 bar...
  11. K

    Caculating the enthelpy change of reaction from delta T values(experimentally)

    Hi! Thanks for your interest in this this post :D! So two reactions I performed were: A) Adding 50 cm3 water to 0.025 moles CuS04 and measuring ΔT. B) Adding 50 cm3 water to 0.025 moles CuS04.5H2O and measuring ΔT. Well turns out the calculations were wrong, since I apparently didn't get...
  12. M

    Can Sinc Functions Serve as Nascent Delta Functions for Non-Smooth Integrands?

    greetings . i have two questions regarding the sinc function in the week limit , where it can be used as a nascent delta function. the definition : \lim_{\varepsilon \rightarrow 0}\frac{1}{\pi }\int_{-\infty}^{\infty}\frac{sin\left(\frac{x-x_{0}}{\varepsilon}\right) }{x-x_{0}}...
  13. N

    The Dirac delta in squere root of the absolute value

    Dear Forum Users, I have got more math question rather then the physics question. Does someone know if: \mid d(x)\mid^2 equals just d(x), here d(x) is just the Dirac delta ? best regards, nykon
  14. N

    Dirac delta wave function impossible?

    Hello, I was under the impression that a dirac delta was a "legitimate" state for a particle: maybe not mathematically, but least physically. But I was recently told by a post-doc in QM that if your particle is in a dirac delta state at one moment, the very next moment the particle is...
  15. C

    Kronecker Delta and Dirac Delta

    Hello PF, When I was studying Quantum mechanics, I realized that this equality should be true, <{\psi}_{n} \mid {\psi}_{m}>=\int {\psi}_{m}^*{\psi}_{n}dx={\delta }_{mn} So {\psi}_{m}^*{\psi}_{n} must be equal to dirac delta function so that we provide the kronecker delta as a solution of...
  16. A

    Does the dirac delta function have a Laplace transform?

    If yes, how can we find it?
  17. J

    Doubt about the kronecker delta

    Well I don't understand this equality: A^{j}_{i}*A_{j}^{k}=\delta_{i}^{k} It is true because it is the result of a calculation. But assuming it is true ¿What happens if one of the A_{i}^{j} is zero?. Then it does not matter which is the value of the A_{j}^{k} the equality will be false...
  18. H

    The Discontinuity of Wave Functions in a Dirac Delta Potential

    consider a particle in one dimention. there is a dirac delta potential such as V=-a delat(x) the wave functions in two sides(left and right) are Aexp(kx) and Aexp(-kx) respectively. so the differential of the wave functions are not continious at x=0. what is the justification here?
  19. I

    What does a delta symbol mean in mathematics?

    In Spivak's calculus book he provides a proof for: Theorem: If f is continuous on [a, b] and f(a) < 0 < f(b), then there is some number x in [a, b] such that f(x) = 0. In the proof he explicitly says, "...A has a least upper bound \alpha and that a < \alpha < b. We now wish to show that...
  20. M

    Fourier Trasform of Delta functions

    Hi All, I am trying to understand more rigorously why the Fourier transform of a constant functions equals the Dirac delta distribution. I found somewhere this is justified by imposing the self-adjointness, so that under a duality pairing <..,..> and indicating with F(f) the transform of...
  21. L

    Use of Dirac delta to define an inverse

    I was wondering which are the properties of functions defined in such a way that ∫dx f(y-x) g(x-z) = δ(y-z) where δ is Dirac delta and therefore g is a kind of inverse function of f (I see this integral as the continuous limit of the product of a matrix by its inverse, in which case the...
  22. B

    How to integrate the delta function of complex variable?

    It is easy to integrate the delta function of real variable. But when the argument of the delta function is complex, I get stuck. For example, how to calculate the integral below, where u is a complex constant: \int_{ - \infty }^{ + \infty } {f\left( x \right)\delta \left( {ux}...
  23. K

    Solving Epsilon Delta Proof: |x^2 - 9| < ε

    Homework Statement if |x-3| < ε/7 and 0 < x ≤ 7 prove that |x^2 - 9| < ε Homework Equations The Attempt at a Solution So ths is what I did so far. |x+3|*|x-3| < ε (factored out the |x^2 - 9|) |x+3|*|x-3| < |x+3|* ε/7 < ε (used the fact that |x-3| < ε/7) |x+3|* ε/7 *7 <...
  24. K

    Thermochemistry- Finding Delta G

    Homework Statement Calculate Delta G Degree for 2Mg(s) + O2(g) -> 2MgO(s) Homework Equations Delta G = (Delta G of products - Delta G of reactants) The Attempt at a Solution So according to my book's appendix, the dG of Mg is 0, the dG of O2 is 0, and the dG of MgO is -596.6...
  25. L

    Does Dirac manipulate his Delta function sensibly?

    In the Principles of Quantum Mechanics, Dirac derives an identity involving his delta function: xδ(x)=0. From this he concludes that if we have an equation A=B and we want to divide both sides by x, we can take care of the possibility of dividing by zero by writing A/x = B/x + Cδ(x), because...
  26. A

    An ODE involving delta function

    x''+2x'+x=t+delta(t) x(0)=0 x'(0)=1 The textbook, "Elementary differential equations" by Edwards and Penney, gives the answer as -2+t+2exp(-t)+3t exp(-t) It is clearly wrong, as in this case x'(0)=2, not x'(0)=1.
  27. sunrah

    What is the Application of Dirac Delta in Charge Constellations?

    Homework Statement We have to give the total charge, dipol and quadrupol moments of a charge constellation, but I seem to be falling at the first hurdle. Q = \frac{1}{4\pi \epsilon_{0}} \int_{vol} \rho(\vec{r}) d^{3}\vec{r} whereby the charge density of the group of particles is...
  28. J

    Delta Epsilon Proof of a Limit

    Homework Statement Prove, using the formal definition of limits: If http://rogercortesi.com/eqn/tempimagedir/eqn4201.png and c>0, then [PLAIN]http://rogercortesi.com/eqn/tempimagedir/eqn4201.png (add the constant beside f(x) here, I couldn't get the equation generator to cooperate)...
  29. J

    Can δ-ε Definitions Prove This Infinite Limit Scenario?

    Homework Statement Prove, using the formal definition of limits: If lim (x->inf) g(x) = inf and g(x) leq f(x) for x->a, then lim (x->a) f(x)=inf. leq = less than or equal to. Homework Equations The Attempt at a Solution Honestly, I'm not even sure where to start on this one. Anyone bored...
  30. sunrah

    Energy density (electrodynamics/ Dirac delta etc)

    So I have the following velocity vector of a charged particle in an EM field \dot{\vec{r}} = (v_{0x}cos(\alpha t) - v_{0z}sin(\alpha t), \frac{qEt}{m} + v_{0y}, v_{0z}cos(\alpha t) + v_{0x}sin(\alpha t)) and I have to state the energy density, which is defined as follows: \tau =...
  31. D

    Why is the derivative of the sign function equal to Dirac's delta function?

    Hi! I'm having some difficulties understanding WHY sign function's derivative actually is dirac's delta function? Or more specifically why the derivative equals one at zero and NOT infinite, as the sign function's "actual" derivative at zero equals infinite? Atleast it would make sense. Thanks...
  32. U

    Calculating Energy Uncertainty for a Particle Described by a Wave Function

    Homework Statement Determine the energy uncertainty \Delta E = \sqrt{<E^2> - <E>^2} for a particle described by a wave function \Psi (x) = c_1 \psi (x)_1 + c_2 \psi (x)_2 where \psi_1 and \psi_2 are different (orthonormal) energy eigenstates with eigenvalues E_1 and E_2. Homework...
  33. AlexChandler

    Delta Function Bound State

    Homework Statement A particle moves in one dimension in the delta function potential V= αδ(x). (where that is an 'alpha' ... not 'a') An initial wave function is given \Psi = A(a^2-x^2) for x between -a and a and Psi=0 anywhere else What is the probability that an energy measurement will...
  34. J

    Double Delta Fuinction Potential - Tell me if Im correct please

    Homework Statement THIS IS THE QUESTION V (x) = \sqrt{((h-bar ^{2})V_{0})/2m} [\delta(x-a)+ \delta(x+a)] -How do I find R and T? -Under what condition is there resonant transmission? 2. The attempt at a solution ok. I got these answers. Are these correct? Someone please...
  35. K

    Does anybody know a site where i can find many epsilon delta problems?

    I'm sick of still not getting this. I bombed the epsilon delta part of my mid term. A site where it gives many problems on epsilon delta and solutions would be amazing.
  36. J

    Double Delta Function Potential

    I have V (x) = \sqrt{((h-bar ^{2})V_{0})/2m} [\delta(x-a)+ \delta(x+a)] How do I find R and T? Under what condition is there resonant transmission?
  37. J

    Dirac delta function in reciprocal function

    From dirac, if A=B, then \frac{A}{x}=\frac{B}{x}+c\delta(x) (1) How this formula is derived? Since \frac{dlnx}{dx} = \frac{1}{x}-i\pi\delta(x) We can get \frac{A}{x} = A\frac{dlnx}{dx}+Ai\pi\delta(x) \frac{B}{x} = B\frac{dlnx}{dx}+Bi\pi\delta(x) So if A=B, \frac{A}{x}=\frac{B}{x}...
  38. T

    How does multiplying by delta theta relate to spherical coordinates?

    Hi, I'm reading through one of my books and it's explaining how a vector is eqaul to multiplying sin\phi and \Delta\vartheta. the way it's written in the text is as followed, |\Deltai| \approx (sin\phi)\Delta\vartheta I have never understood how things like this work. Could...
  39. N

    1D delta funtion potential well

    Hello forum, I have a question regarding the delta function potential well. Given the following potential: V(x) = -αδ(x) for -a/2 < x < a/2 (α- positive constant) and V(x) = 0 elsewhere, how would one show that the ground state is the only eigenstate with E <0. One could of course solve the...
  40. J

    Dirac delta function in reciprocal function

    From dirac, if A=B, then \frac{A}{x}=\frac{B}{x}+c\delta(x) (1) How this formula is derived? Since \frac{dlnx}{dx} = \frac{1}{x}-i\pi\delta(x) We can get \frac{A}{x} = A\frac{dlnx}{dx}+Ai\pi\delta(x) \frac{B}{x} = B\frac{dlnx}{dx}+Bi\pi\delta(x) So if A=B, \frac{A}{x}=\frac{B}{x}...
  41. J

    Delta dirac function times zero

    Let δ(x)=∞ at x = 0, and zero elsewhere. Then δ(x)(1-exp(x)) = ? It seems the above expression is zero. But isn't it zero times infinity at x = 0?
  42. V

    Star Delta Conversion: Why Phase Shift?

    Why there is a phase shift of 30 degree (positive or negative) if we convert our winding from star to delta or vice versa?
  43. W

    The Alternate form of the Dirac Delta Function

    Hello, I am trying to show that: \delta(x) = \lim_{\epsilon \to 0} \frac{\sin(\frac{x}{\epsilon})}{\pi x} Is a viable representation of the dirac delta function. More specifically, it has to satisfy: \int_{-\infty}^{\infty} \delta(x) f(x) dx = f(0) I know that the integral of...
  44. F

    Understanding Multiple Delta Function in 1D and Multidimensional Spaces

    Hi everyone, I have trouble understanding the multiple delta function. For one dimensional delta function, we have δ(\varphi(x))=\sum_{i=1}^{N}δ(x−xi)|\varphi′(xi)| where xi's (for i = 1 to N) are simple zeros of f(x) and it is known that f(x) has no zeros of multiplicitiy > 1 but...
  45. R

    Wavefunction collapse and dirac delta functions

    What is the experimental evidence that a wavefunction will collapse to a dirac delta function, and not something more 'smeared' out?
  46. N

    I don't understand q = mc delta T

    Well, I understand q = mc∆T, along with q = mHv and q = mHf What I don't understand is this graph: http://dinosaurtheory.com/phase_change.jpg Well, I mean, I understand THAT graph. Here's what I don't understand: Today in chemistry, we received a very similar graph, but the X-axis was...
  47. N

    Need help proving a limit using epsilon delta definition.

    Need help proving lim(x)->(a) sqrt(x)=sqrt(a) using epsilon delta definition. Homework Statement Prove that the limit of \sqrt{x} is \sqrt{a} as x approaches a if a>0 Homework Equations in words By the epsilon delta definition we know that the distance between f(x) and the limit...
  48. J

    How Do You Solve a Beginner's Epsilon-Delta Proof for 1/x?

    Homework Statement This is my first delt/epsilon proof ever, so please understand if I seem ignorant. e=epsilon d = delta Let f(x) = 1/x for x>0 If e is any positive quantity, find a positive number d, which is such that: if 0 < |x-2| < d, then |f(x) - 1/2| < e Homework...
  49. M

    Dirac Delta from Continous Eigenfunctions

    In the equation for determining the coefficients of eigenfunctions of a continuous spectrum operator, I have trouble understanding the origin of the Dirac delta. a_f = INTEGRAL a_g ( INTEGRAL F_f F_g ) dq dg a is the coefficient, F = F(q) is an eigenfunction. From this it is shown that...
  50. khurram usman

    Epsilon and delta method of finding limits?

    first of all i don't know anything about this epsilon and delta method.explain this a bit. secondly i have been given a problem involving this method: f(x)=x^2 given: limit x-->2 [x^2] = 4 a) what is the value of x' such that f(x')= 4 + .01? find \delta=x'-2 b) what is the value of...
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