Delta Definition and 999 Threads

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...

[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...

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...

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...

[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...

[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)...

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]...

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...

is there a form to define the dirac delta function for complex values ? i mean \delta (x-a-bi) or \delta (-ix) using 'test functgions' i get that they converge nowhere (always infinite) which makes no sense at all, using scalling properties we could define \delta (ix) = \delta(x)...

Does anyone know what the Dirac delta function would look like in a space with curvature and torsion? The Dirac delta function is a type of distribution. But that distribution might look differently in curved spacetime than in flat spacetime. I wonder what it would look like in curved spacetime...

Alright...so I've got a question about the convolution of a dirac delta function (or unit step). So, I know what my final answer is supposed to be but I cannot understand how to solve the last portion of it which involves the convolution of a dirac/unit step function. It looks like this: 10 *...

Alright, I'm in my first QM course right now, and one of the topics we've looked at is solving the one-dimensional time-independent Schrödinger equation for various potentials, such as the harmonic oscillators, infinite and finite square wells, free particles, and last, but not least, the dirac...

Homework Statement The function \delta(cosx) can be written as a sum of Dirac delta functions: \delta(cosx)=\sum_{n} a_{n}\delta(x-x_{n}) Find the range for n and the values for a_{n} and x_{n} The Attempt at a Solution Well, taking the integral of \delta(cosx), we only get spikes when...

Homework Statement R = { (X,Y) \epsilon P(A) x P(A) / (X\DeltaY) \subseteq B} (X\DeltaY) \subseteq B - what does delta mean? Homework Equations The Attempt at a Solution

Homework Statement I would like to prove that \delta(ax)={\delta(x) \over {|a|}}. My problem is that I don't know how the absolute value brackets arise. Homework Equations \int_{-\infty}^{\infty} \delta(x)dx = 1The Attempt at a Solution I start from \int_{-\infty}^{\infty} \delta (ax) dx, and...

with limits from 0 to 1 \int delta(x) * cos(x) dx does this delta function integral even make sense from 0 to 1?

The Dirac delta function, \delta (x) has the property that: (1) \int_{-\infty}^{+\infty} f(x) \delta (x) dx = f(0) Will this same effect happen for the following bounds on the integral: (2) \int_{0}^{+\infty} f(x) \delta (x) dx = f(0)...

Hello, I'm having trouble finding the rest energy of delta, on the internet. Can anyone give me this value please. It's delta zero. i.e. its charge is 0 and strangeness is 0 too. Thanks a lot for your time From Steven

I’m going to say from the beginning that I need to hand this problem in. I'm not looking for the answer, I think I already have it, just want a critical eye. I need someone to look over this problem and tell me if it's good. Not just if it's right but if it's perfect. I always get the...

Homework Statement Is this the right direction to prove Given that , prove that . Using the delta epsilon definition to prove that means that, for any arbitrary small there exists a where as: If we choose any constant for (x) called C, as long as C does not equal zero, the...

I have a line charge of length L and charge density /lambda on the Z-axis. I need to express the charge density in terms of the Dirac Delta function of theta and phi. How would I go about doing this?

Homework Statement i have a couple of questions to anser and they start 'Give epsilon - delta proofs that the following functions are continuous at the indicated points.' im guessing its not going to be too hard but what is the name of this epsilon - delta proof so i can search for and...

I am trying to evaluate the following integral. \int_{-\infty}^{\infty}{\delta(2t-3)\sin(\pi t) dt} where delta represents the Dirac delta function. I am told that the answer is -1. However, when I evaluate it in MATLAB and Maple 11, I get an answer of -1/2. What is the correct way...

Homework Statement Can u pls help me to prove delta function. Here is the problem in attachment. Homework Equations The Attempt at a Solution

Homework Statement Prove: \lim_{x \to a} \sqrt{x} = \sqrt{a}, if a>0 Homework Equations |f(x)-L| < \epsilon |x-a| < \delta The Attempt at a Solution |\sqrt{x}-\sqrt{a}| < \epsilon, when |x-a| < \delta |x - 2\sqrt{x}\sqrt{a}-a| < \epsilon^2, when |x-a| < \delta From here I...

Homework Statement I'm trying to prove that \delta'(y)=-\delta'(-y). Homework Equations The Attempt at a Solution I'm having trouble getting the LHS and the RHS to agree. I've used a test function f(y) and I am integrating by parts. For the LHS, I have...

Can you force older cells to express more delta protein? Would the cells expressing more delta protein be good or bad?

Could someone please give me a walkthrough of the following question(and answer)?? I really can't understand it... lim x^2 = 9 x->3 if 0<|x-c|<delta then |f(x) - L|< epsilon so... x^2 - 9 = (x+3)(x-3) |x^2 - 9| = |x+3||x-3| Here's the problem.The book states: An...

Homework Statement Solving a problem about the variational method I came across one nasty integral. Here goes: \bar{H} := \frac{ < \hat{0} | H | \hat{0} > }{< \hat{0} | \hat{0} >} Homework Equations H = -\frac{ \hbar^2 }{2m} \frac{\partial ^2}{\partial x^2} + \frac{1}{2} m...

help me please I am in WAS and i need to know Delta V. please please please. ok i am curently in WAS(wa arowspace scolars) I am a bad speller but i could care less also I am new hear. i know what the formula for delta v is but i do not understand it. i am interested in learning but please putin...

Homework Statement Hi there, I'm stuck at a problem where I have (sorry i don't know how to use mathtype so I'll try my best at making this clear) the integral of a dirac delta function squared: int[delta(x*-x)^2] between minus infinity and infinity (x*=constant) I know that the function...

So what we have so far is that any and all subsets are implied by a set. If there exist a set, then all the subsets within it are implied to exist also. This includes the elements of a set. The elements of a set are implied by the existence of a set. One of the most natural things to do with...

Dirac Delta Function: If, at time t =a, the upper end of an undamped spring-mass system is jerked upward suddenly and returned to its original position, the equation that models the situation is mx'' + kx = kH delta(t-a); x(0) = x(sub zero), x'(0) = x(sub 1), where m is the mass, k is the...

Homework Statement Please don't make fun of my question, I just want to have a strong understanding of the meaning and it's use My textbook just pops these symbols out at me without explanation. Maybe it just expects I know this stuff In the equation Vs = \Delta d / \Delta t

Homework Statement If we have a delta function in cartesian coords, how do we convert it into spherical. for example : delta (r) = delta(x-x0) delta(y-y0) delta(z-z0) Homework Equations The Attempt at a Solution I used delta (r) = delta(r-r0) delta(cos{theta}-cos{theta0}) delta...

1. The ProblemHomework Statement 4 Parts to the Assignment. Finding the Displacement of a beam assuming w to be constant. 1. Cantilever beam, free at one end. Length =l, Force P applied concentrated at a point distance rl from the clamped end. Boundary Conditions y(0)=0, y'(0)=0, y"(l)=0, and...

Hello everybody First I'd like to thank for the work all of you are developing with this forum. I found it for casuality but I'm sure since now it will be a perpetual partner. I'm a Spanish Physics graduate and I am working about microwave guides and connectors for devices components in...

I have two related questions. First of all, we have the identity: \int_{-\infty}^{\infty} e^{ikx} dk = 2 \pi \delta(x) I'm wondering if it's possible to get this by contour integration. It's not hard to show that the function is zero for x non-zero, but the behavior at x=0 is bugging...

Currently I am enrolled in college level General Chemistry course, and at this time we are working on a project to figure out the delta heat for formation of a specific reaction. The equation is this H2 + CuSO4(aq) ---> Cu(s) + H2SO4. We have gone through and determined the half...

[b]1. Homework Statement \int x[delta(x)-delta(x/3+4)] dx Homework Equations so I'm supposed to use this principle: \int f(x)delta(x-xo)dx=f(xo) The Attempt at a Solution So it seems simple but I just want to make sure that I'm applying the above principle correctly. I...

I understand how an ordinary wing works but I cannot find anything on how a delta wing works, the only thing I know is that it creates vortices on the upper wing surface, but how do these vortices create lift?

[SOLVED] Delta Function Well and Uncertainty Principle Homework Statement Griffiths Problem 2.25. I need to calculate < p^{2}> for the Delta Function Well. The answer given is: < p^{2}> = (m\alpha/\hbar)^2 The wave function given by the book is...

calculate the current through circuit which contain 5 resistors,3 of them shape y network their values are 220 ohm's,330 ohm's,680 ohm's. the other 2 resistors are in parallel with them and they are 1Kohm's. the voltage sourse give 10V.

Homework Statement SO I'm given a dirac delta function, also known as a unit impulse function. d(t-t'_=(1/P) sum of e^[in(t-t')], for n from negative to positive infinity. I need to graph this. Homework Equations I understand that at t', there is a force made upon the system which...

So I'm studying that part right now. I only get parts of it though, it seems. The first thing the book goes over (This is intro to QM by Griffiths) is a potential that has the form -A*deltafunction. Okay, that's just something he plucked for simplicity. But then if the potential is lower...

Homework Statement Why does it make sense that a negative delta function potential represents a highly localized attractive force and a positive delta function potential represents a highly localized repulsive force? How do you explain that using -dV/dx = f(x) ? I guess I am confused about...

I'm trying to plot the function f(x,y) = DiracDelta[r-r0]and then take the Fourier transform. Is this a radial delta function? I'm having trouble understanding the significance of this "function" . Thanks!

Q: Integral of Delta(x-b)dx and the lower limit is (-) infinity and upper is a Please help me in steps tried my best to solve.Note this is not homework I was doing the book problems or my practice Thanks

for linear time invariant system, y(t)=h(t)*x(t) where y(t) is the output , x(t) is the input and h(t) is the impulse response.(* is the convolution) The definition of convolution is y(t)=integration from -infinity to +infinity (h(tau)x(t-tau)d(tau) p/s: i don't know how to use...

Homework Statement Hans stands at the of the Grand Canyon and yodels down to the bottom. He hears his yodel echo back from the canyon floor 5.20s later. Assume that the speed of sound in air is 340.0m/s. How deep is the canyon at this location? I made a chart. Velocity Original = 340...