Delta Definition and 1000 Threads

I've been thinking about the properties of the Dirac delta function recently, and having been trying to prove them. I'm not a pure mathematician but come from a physics background, so the following aren't rigorous to the extent of a full proof, but are they correct enough? First I aim to...

Homework Statement Having trouble understanding dirac deltas, I understand what they look like and how you can express one (i.e. from the limiting case of a gaussian) but for the life of me I can't figure out why the results of some integrals featuring dirac deltas equate to what they do...

For a research project, I have to take multiple derivatives of a Yukawa potential, e.g. ## \partial_i \partial_j ( \frac{e^{-m r}}{r} ) ## or another example is ## \partial_i \partial_j \partial_k \partial_\ell ( e^{-mr} ) ## I know that, at least in the first example above, there will be a...

I have a potential which is zero everywhere except at -2a , -a , 0 , a , 2a on the x-axis where there is an attractive delta potential at each of the 5 points. I know there is a maximum of 5 bound states. I know there can be no nodes for |x| > 2a and a maximum of one node between each delta...

Homework Statement ∫δ(x3 - 4x2- 7x +10)dx. Between ±∞. Homework EquationsThe Attempt at a Solution Well I don't really know how to attempt this. In the case where inside the delta function there is simply 2x, or 5x, I know the answer would be 1/2 or 1/5. Or for say δ(x^2-5), the answer would...

I manufacture heating elements and a customer wired a delta heater in parallel with a wye heater. They claim that this lowers the overall resistance of the delta thus causing this element to draw more amps than what it was designed for. I disagree and do not see how the heater is eternally...

Given: Assume that f (x) is continuous at x = 0 and vanishes as x→±∞. Hint. Replace x by y/n and take lim n→∞ before integrating. I apply the hint and get $ \frac{1}{\pi}\int_{-\infty}^{\infty} \,{\lim_{{n}\to{\infty}}}{\frac{sin y}{y}} \,dy $ For the limit, as n -> ${\infty}$ , y -> 0. By...

Basically I want to test my analog circuit using a forcing function that has a form of a delta function. The function generator I use outputs sine wave, triangular wave and square wave (+ve and -ve output in one period). Are there any ways to produce a square wave that has an output for like 5%...

I don't see how the kronecker delta function is linear, and hence I don't see how it can serve as a dual basis for a ket space. How is the kronecker delta linear? How can it serve as a dual basis?

I'm trying to solve the following equation (even if I'm not sure if it's well posed) \partial_{x} \, y(x) + a(x)\, y(x) = \delta(x) with ##\quad \lim_{x \rightarrow \pm \infty}y(x) = 0## It would be a classical first order ODE If it were not for the boundary conditions and the Dirac...

I feel like a ping pong ball on the question of whether or not total energy of a pair of electrons changes when they become entangled or disentangled. I began with a mental model similar to electrons in orbitals. Emit a photon and drop into a lower energy state until reading the ground state...

lim(9-x) as x->4 = 5 I thought I was supposed to do this: 9-4=5 5=5 But apparently I was supposed to use delta and epsilon? I'm not sure how to find either of these. I know you find epsilon first but I'm really confused so if anyone knows just HOW to find it, that would be extremely helpful...

Given a function f(x), a point x0, and a positive number E (epsilon), write the limit then find delta>0 such that for all x 0< |x-x0| < delta -> |f(x)-L| < E f(x) = 3-2x, x0=3, E=.02 Here is my attempt: Lim (3-2x) as x->3 = -3 -.02 < |3-2x - 3| <.02 -.02 < |-2x| < .02 .01 > x > -.01 -2.99 > x-3...

The website rules say that when people help they are not allowed to include answers? But how am I supposed to check my answers... anyone else have this problem?

Hello

Hey everybody, I'm an engineering Ph.D. so my knowledge of n-dimensional Euclidean spaces is lacking to say the least. I'm wondering what sort of approach I can take to solve this problem. ##\boldsymbol{1.}## and ##\boldsymbol{ 2. }## I am given a probability distribution for a random...

My teacher constantly stresses that 10 moles of a gas going to 11 moles of a gas will ALWAYS cause an increase in entropy (ΔS>0). But why? For example (I know that O2 shouldn't technically be a liquid, but just as an example): 2H2O(g)⇔H2O(g)+(3/2)O2(l)+2H2 It seems iffy to me. We go from...

Homework Statement Evaluate the integrals in the attached image Homework EquationsThe Attempt at a Solution

I am trying to figure out the difference between Δ0 and Δ- and the proton and neutron since both appear to have the same combinations of up/down quarks. Deltas have isospin 3/2 and spin angular momentum 3/2 whereas protons and neutrons have isospin 1/2 and spin angular momentum 1/2. I'm...

Homework Statement "Use the given graph of f(x) = x^2 to find a number delta such that..." Homework Equations If ##([\lim_{x \rightarrow a} f(x)] - L)## then there exists an ##\epsilon## such that ##[0 < |x - a| < \delta] \Rightarrow [|f(x) - L| < \epsilon]##. Here, f(x) and ##\epsilon##...

Show by direct calculation that Eqs. (4-134) and (4-137) in the textbook by Duderstadt and Hamilton hold, i.e.:(a) ∫ dΩΩiΩj= 4π/3 δij; i,j = x,y,z; 4π(b) ∫ dΩΩxΩyΩz = 0, if l, m, or n is odd. 4π The integrals are over 4π. This is part of the derivation of the diffusion equation...

The question asks to solve for delta S surroundings at 298K when 2.49 moles of H2S (g) react. reaction: 2H2S (g) + 3O2 (g)= 2H2O (g) + 2SO2 (g) My problem is that I don't know how to calculate delta S surroundings. So to solve the problem I'm making the assumption that -Delta S surroundings =...

Homework Statement Solve the integral ## \int_0^{3\pi} \delta (sin \theta) d\theta## Homework EquationsThe Attempt at a Solution I can rewrite ## delta (sin \theta) ## as ##\sum_{n=-\infty}^{\infty} \frac{\delta(\theta - n\pi)}{|cos (n\pi)|}=\sum_{n=-\infty}^{\infty} \delta(\theta-n\pi)## So...

Homework Statement Consider an uni-dimensional scattering by a delta function at the origin, given by the potential ##V(x) = g \delta(x)##, with ##g>0##. Using the following result, with ##G(x)## being the green function: $$\Psi (x) = e^{ikx} + g...

Homework Statement Prove lim_{x->\frac{1}{10}}\frac{1}{x}=10 Homework Equations |f(x)-L|<epsilon, |x-a|<delta The Attempt at a Solution I need to go from 1/x to x, so I applied an initial condition of delta<1/20 \frac{-1}{20}<x-\frac{1}{10}<\frac{1}{20} \frac{1}{10}<x<\frac{3}{10}...

does anyone know how to program a delta hmi a series

Homework Statement Break integral into positive and negative, integrate, recombine and simplify and show that it reduces to a real-valued function. (See attachments) Homework Equations See attachments The Attempt at a Solution My solution is not reducing to a real-valued function. Please see...

Homework Statement For the balanced three-phase loads shown in FIGURE 3, ZY = (15 + j15) Ω and ZΔ = (45 + j45) Ω. Determine: Uploaded file C1.png (a) the equivalent single Δ-connected load, (b) the equivalent single Y-connected load obtained from the Δ-Y transformation of (a) above, (c) the...

I know what is it but I can't figure out the rationale behind it. As in why do we need it? Moreover I don't know how to represent it in terms of kronecker delta. How do you do that?

Hi, For my math methods 3 course, I am not quite sure which books to use. The course is based on the math methods book by Riley, Hobson, and Bence, and I don't particularly like it. Hence, I am looking for some alternatives. Especially for the Preliminaries section. I had a real hard time...

A satellite changes its orbit inclined 66° at 260.0 km altitude to a polar orbit at the same altitude. What Delta V was required? ... I am stuck. do I figure it out using: DeltaV1 = |V_transfer at orbit 1 - V_orbit 1| and DeltaV2 = |V_transfer at orbit 2 - V_orbit 2| or is there another...

Does Ross's book teach and/or use Epsilon-delta proof techniques?

Homework Statement Homework EquationsThe Attempt at a Solution a) the question is to transform star to delta ?

I am currently having some issue understanding, what you may find trivial, epsilon-delta proofs. I have worked through Apostol Vol.1 and ran through Spivak and I found Apostol just uses neighborhoods in proofs instead of the epsilon-delta approach, while nesting neighborhoods is 'acceptable' I...

sir, 1)star connection 3ph motor(415V) which load location is suitable? 2)delta connection 3ph motor(415V) which load location is suitable? 3)star&delta connection 3ph motor(415V) which load location is suitable? please support me.

Hopefully this has not already been asked. It would be hard to do a forum search with the right words to find it if it has been already. I am wondering if it is ever possible or common place to generate power in a Wye generation scheme and then connect it directly to a transformer with a...

Homework Statement I am having trouble understanding this: I have a Dirac Delta function $$ \delta (t_1-t_2) $$ but I want to prove that in the frequency domain (Fourier Space), it is: $$\delta(\omega_1+\omega_2) $$ Would anyone have any ideas how to go about solving this problem? I know...

Homework Statement Find the delta x of the bow pullback. The weight of the pullback is 45 kg, the speed of the arrow as it shot out was 184mph( i converted that to velocity and got 83 m/s). Homework Equations I'm using K1+U1+W=K2+U2. The Attempt at a Solution I wasn't sure which formulas to...

Homework Statement This problem came when I was learning the Poisson's equation (refer to http://farside.ph.utexas.edu/teaching/em/lectures/node31.html). when it came to the step to find the Green's function G which satisfies \nabla^2 \cdot G(\textbf{r}, \textbf{r}') =...

Homework Statement Why does ##\Delta H=\pm |q_{surroundings}|##? Homework EquationsThe Attempt at a Solution Exothermic reactions have a ##-\Delta H## but does that mean that ##q## is a ##+q##. Vice versa for a endothermic reaction. I get confused on which sign i should use for which when i do...

I last studied maths in school 10 years ago and we never used any Greek letters. 1. Homework Statement Talking about contingency in classical conditioning in psychology. The sum is a calculation that people and animals seem to do in their heads to work out the probability that two stimuli...

Homework Statement x(t) = cos(3πt) h(t) = e-2tu(t) Find y(t) = x(t) * h(t) (ie convolution) Homework Equations Y(s) = X(s)H(s) and then take inverse laplace tranform of Y(s) The Attempt at a Solution L(x(t)) = [πδ(ω - 3π) + πδ(ω + 3π)] L(h(t)) = \frac{1}{s+2} Laplace Transform inverse ...

Dear Friends, I need technical solution for my problem; Specification: I have two motors, type: 1. HCT/ATEX 45-2T-2 (R/MIN=2800), (400V-3,60A), (KW-1,50) 2. HCT/ATEX 45-2T-3 (R/MIN=2860), (400V-5,00A), (KW-2,20) Also, every motor has its own inverter: Inverters are from INVERTEK DRIVES...

Hi, it's actually not homework but a part of my research. I intuitively see that: \lim_{t \rightarrow \infty} \frac{sin^2[(x-a)t]}{(x-a)^2} \propto \delta(x-a) I know it's certainly true of sinc, but I couldn't find any information about sinc^2. Could someone give me a hint on how I could...

How do you calculate how much delta v is lost from gravity and atmospheric drag? I've been looking for days but I can't find anything that actually tells me how it's calculated. For example it takes 1.5 km/s - 2 km/s extra delta v for a low Earth orbit because of drag loss, how was that number...

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...

Hi, Suppose you want to prove |x - a||x + a| < \epsilon You know |x - a| < (2|a| + 1) You need to prove |x + a| < \frac{\epsilon}{2|a| + 1} So that |x - a||x + a| < \epsilon Why does Michael Spivak do this: He says you have to prove --> |x + a| < min(1, \frac{\epsilon}{2|a| + 1}) in...

hi deoes anyone know any online resource for proofs of Dirac delta function identities and confirming which representations are indeed DD functions Thanks a lot.

Homework Statement Integrate $$\int_V \delta^3(\vec r)~ d\tau$$ over all of space by using V as a sphere of radius r centered at the origin, by having r go to infinity. Homework EquationsThe Attempt at a Solution This integral actually came up in a homework problem for my E&M class and I'm...

Hi all, I am trying to develop a motor protection scheme for the following scenario. There are two 3.3kV 250kW delta connected motors close coupled to a gearbox driving a crusher. Both have separate DOL starters and protection systems. What happens to the motor current in a motor that loses a...