Delta Definition and 1000 Threads

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...

Homework Statement Evaluate: \int_{-3}^{5} e^{-2t} sin(t-3) \delta(t-5) dt Homework Equations \int_{-\infty}^{\infty} f(t) \delta(at-t_0) dt = \frac{1}{|a|}f(\frac{t_0}{a}) The Attempt at a Solution e^{-2(5)} sin (5-3) = e^{-10} sin (2) The solution given by the professor...

Homework Statement How would one show that dirac delta is the limit of the normal distribution? http://en.wikipedia.org/wiki/Dirac_delta using the definition \delta(k) = 1/(2\pi)\int_{-\infty}^{\infty}e^{ikx}dx Homework Equations The Attempt at a Solution

Evaluate: \int^{\infty}_{-\infty} f(x)\delta(x-x_0)dx Where f(x)=ln(x+3), x_0=-2 Ordinarily, you would just evaluate f(x_0), so it would be 0, but in this case, since f(x) is -\infty at x=-3, does that make a difference?

Homework Statement I'm having some trouble understanding the Kronecker Delta function and how it is used. I understand the basics of it, if i=j, delta=1, if not, delta=0. However, I don't understand why: \delta_{ii}=3 and \delta_{ij}\delta_{ij}=3Homework Equations \delta_{ij}=...

Quick question about a discrete unit impulse. If I were to draw delta[n+1], at ... etc n = -2 ... the point would be at location: 0 n = -1 ... the point would be at location: 1 n = 0 ... the point would be at location: 0 n = 1 ... the point would be at location: 0 n = 2...

Homework Statement \int^{A}_{-A}\int^{Bx}_{-Bx}c\delta(xcos\varphi+ysin\varphi-d)dydx where A, B, c, d are constant Homework Equations The Attempt at a Solution I have tried a few different ways to integrate this, but am completely confused with what happens to this kind of delta...

OK, I'm currently reading Hughes' Finite Element Method book, and I'm stuck on a chapter the goal of which is to prove that the Galerkin solution to a boundary value problem is exact at the nodes. So, the author first speaks about the Dirac delta function: "Let \delta_{y}(x) = \delta(x-y)...

Why in some sites, the work appears like \ \ \delta W instead of dW ? Whats the differences between \ \delta W and dW?thanks

Hello, how would you derive the solutions of the twin delta function potential: V(x) = -g \delta(x+a) + \delta(x -a ) ? Obviously the solutions outside the potential are Ae^Kx for x less than aand A e^-Kx for x greater than a. But how do you derive the hyperbolic cosine function for the...

I have seen two formulations of the dirac delta function with the Fourier transform. The one on wikipedia is \int_{-\infty}^\infty 1 \cdot e^{-i 2\pi f t}\,dt = \delta(f) and the one in my textbook (Robinett) is 1/2\pi \int_{-\infty}^\infty 1 \cdot e^{-i f t}\,dt = \delta(f) I...

I do not know if it is true but is this identity true \frac{\delta _{n}^{x} }{h} \rightarrow \delta (x-n) as h tends to 0 ?, the first is Kronecker delta the second Dirac delta. i suspect that the above it is true but can not give a proof

Dear all I'm wondering if you can help me find the most general formula of all nascent delta functions. all i have found a somewhat random forms . I'm looking for a general elegant formula that all the forms can be derived from . thanks in advance .

We know that div \; (\hat{r} / r ) = 4 \pi \delta (r) Why is there no generalized function (distribution) for div \; (\hat{r} / r^2) = ??

Dirac developed his delta function in the context of QM. But there are various functions under the integral that give the delta function. My question is does one Dirac delta function equal any other? Are all ways of getting the Dirac delta function equivalent? Thanks.

Fourier transforms were invented before dirac delta functions but hidden in every Fourier transform is a dirac delta function. But it went unnoticed until dirac came along? Then they argued for the legitamacy of the delta function but it is present in every Fourier transform which is legitamate.

I'm currently reading Griffith's book on time independent Schroedinger's equation about delta functions. However, I complete dislike how the book deals with the delta distribution. firstly, the book discusses how to solve: -\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2}-\alpha\delta\psi=E\psi for...

Okay, so how do you know when to put a delta symbol in front of a variable? For example, U=\frac{3}{2}nRT however, it can also be written as \Delta U=\frac{3}{2}nR\Delta T --Change in Internal energy of a system I'm pretty sure that this isn't the case for many equations such as: \Delta...

Homework Statement prove: lim n-> inifity Sn = 0 Let Sn = (n+1)/(n^2 +1) Homework Equations (for all epsilon > o) (there exists N) (for all n) [ n>N => |Sn-0| < epsilon] The Attempt at a Solution i let epsilon be arbitrary, so we must show that there exists an N such that...

is the formula below valid to calculate the lift coefficient for a delta wing? Cl=2*L/(rho*v^2*A) L=lift (N) rho= air density v= air velocity A=wing area im doing a subsonic wind tunnel project where I am going to measure the lift for a low aspect ratio delta wing. should i use...

Using the Einstein summation convention... Why is \mathbf{a}^2 \mathbf{b}^2 not the same as 3 a_i a_j b_j b_i = 3(\mathbf{a} \cdot \mathbf{b})^2 given that \mathbf{a}^2 = a_i \cdot a_i = a_i a_j \delta_{ij} \mathbf{b}^2 = b_i \cdot b_i = b_i b_j \delta_{ij} and...

Homework Statement A particle with mass M is moving in a spherical delta-potential well, V(r)=-Vo*delta(r-a); Vo>0, a>0 Find the minimum Vo value so that there is at least 1 bounded eigenstate for the particle. Homework Equations looking through my quantum book (griffiths of course)...

the Kronecker Delta function is What does it mean when the subscript is not i,j but i+j?

Homework Statement int[d(x-a)f(x)dx]=f(a) is the dirac delta fn but is int[d(a-x)f(x)]=f(a) as well? If so why?The Attempt at a Solution Is it because at x=a, d(0)=infinite and integrate dirac delta over a region including x=0 when d(0) is in the value in the integral will produce 1 hence f(a).

for OCL- and HOCL

do i have to use this formula Delta G=delta h- t*delta s or could i calculate it like i calculate delta h, products - reactants

A sample of 6.0 mol N2 is originally confined in 30 dm^3( ie L) at 273K and then undergoes adiabatic expansion against a constant pressure of 95kpa until the volume has increased by a factor of 2.0. calculate q,w,delta T, Delta U and Delta H (The final pressure of the gas is not necessarily 95...

Delta T > To? I was working on the derivation of the time dilation of Eisteins Special Theory of Relativity, when I realized that your change in time from the final equation is actually higher than the time of the observer at rest. Now I understand why the time an object traveling close to the...

When integrating and differentiating I'm not sure weather to use a lower case delta or just a d. Is there a time when one is more a appropriate then another or does it not even make a difference? Are they to completely different things? I know it might seem trivial but I have no idea which is...

Homework Statement Given that lim f(x)=L as x approaches a , prove that lim (x+f(x))=a+L as x approaches ahttps://www.physicsforums.com/attachments/9630. Your proof cannot assume that the limit of a sum of two functions is the sum of their individual limits. You must use the delta-epsilon...

Hi I am not a mathematician so my question might be silly. I really came across it in physics but I think it is purely mathematical: I came across an equation of the form: delta(m-n)*A= delta(m-n)*B my question is now for what cases can I conclude A=B? Does this only hold for m=n, or can I...

Dear all, I need a simple proof of the following: Let [tex]u \in C(\mathbb{R}^3)[\tex] and [tex]\|u\|_{L^1(\mathbb{R}^3)} = 1[\tex]. For [tex]\lambda \geq 1[\tex], let us define the transformation [tex]u\mapsto u_{\lambda}[\tex], where [tex] u_{\lambda}(x)={\lambda}^3 u(\lambda...

Okay, I decided to start trying to understand the nulceon and delta resonances. Does anyone have suggestions for a good explanation of how these work? How many resonances are there? How are they distinguished? Etc. Here's the PDG information...

I can remember from Differential Equations that any function convolved with a delta function results in a copy of the function located at the impulese. That is, x(t) * \delta(t-5) = x(t-5) However, I can't remember why. This is really irritating me since I need to use this concept for my...

I keep seeing this come up in relativity and tensor resources but I have no idea wht the heck it means. Could someone explain it to me?

Homework Statement Can some one explain why the second derivative of f(x) is (f(x+h)-2f(x)+f(x-h))/h^2? If you take the intervals to be x = 0 to x = 1 and you divide up the segment into little “hs” so that each x=h, 2h, 3h, nh, and so on? I see that first derivatives can be...

It's a nightmare whenever I see physics problems that involve the change of a variable with respect to another change in varible. Say for example, delta-P/delta-H. The pressure increases as the depth of the water increases. And you want to find the pressure at a certain depth. I see that...

Homework Statement find a number delta Homework Equations f(x) = 1/x | 1/x - 0.5 |<0.2 whenever | x - 2 | < delta The Attempt at a Solution how would you factor out a negative exponent? is this possible? i think i can get x out from under the 1/x with using negative...

Homework Statement How many stationary states exist for this potential? What are the allowed energies if the strength of the well, \alpha= \hbar^2/ma and \hbar^2/4ma where a= the position of the well(one at a, one at -a) Homework Equations V(x) = -\alpha(\delta(x+a) +\delta(x-a)) E_{one...

/square rootsign 4x+1/ <.5 /X-2/ < delta 2 is x and 3 is y, 3 goes to 3.5 and 2.5, i need help with the absolute value of the square root sign 4x+1

| √4x-1 -3 | < .5 X-2<delta use graph to find delta, u can draw out the graph which is simple, the 4x-1 is squared, it's just i couldn't fit the square root on it all, now, the coordinates are 2,3 and 3 goes to 3.5 and 2.5 now here's where i get stuck, what do i do with the...

Homework Statement My question asks me to sketch the following: g(x) = \delta (y+a) + \delta (y) + \delta (y-a) Homework Equations The Attempt at a Solution I think this is it, but am I correct? I don't recall actually seeing a delta function other than a Kronicker(sp?) delta...

A vector function V(\vec{r}) = \frac{ \hat r}{r^2} If we calculate it's divergence directly: \nabla \cdot \vec{V} = \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{1}{r^2} \right) = 0 However, by divergence theorem, the surface integral is 4\pi . This paradox can be solved by...

let f(y)=\int_0^2 \delta(y-x(2-x))dx. Find f(y) and plot it from -2 to 2. I know how to calculate \delta (g(x)) but i am not sure how to treat it with the y. I thought possibly to solve the quadratic in the delta function to find what x will equal for the roots in terms of y and got...

https://www.physicsforums.com/showthread.php?t=73447 I saw the above tutorial by arildno and looked at how he defined the Dirac Delta "function" as a functional. But isn't there a more easier way to do this. I have seen the following definition in a lot of textbooks. \delta(t) \triangleq...

I often see this in electrodynamics in the form of a point charge density function. There are some rules on how to manipulate the thing in integrals. But what is it mathematically?

I can't figure out how to integrate this: \int_{0}^{\infty} \frac{x}{\sqrt{m^2+x^2}}sin(kx)sin(t\sqrt{m^2+x^2}) dx m, k and t are constants. The book has for m = 0, the solution is some dirac delta functions.

Can somebody help me out? I'm reading about formulas for cross sections for spin1 particles but I don't understand the delta functions, in calculating the 2particle pahse space psi For example the interaction; A+B -> C+D has the formula; psi= (2pi)^2 delta(Pa+Pb-Pc-Pd) d3Pc d3Pd / 4EcEd...

I found this equation in a field theory book, which I can't figure how it was derived: \delta(x-a) \delta(x-a) = \delta(0) \delta(x-a)

The relationship between free energy and the equilibrium constant is Go = -RT ln K By measuring the pH at various temperatures, the Kb for NH3(aq) was found to be temperature dependent, yielding the following values: temperature (K) Kb 283 1.34 X 10-5 293 1.42 X 10-5 303 1.50 X...