Delta Definition and 1000 Threads

Homework Statement Find the critical points where \alpha = 1. dv/dt = v2 + \alphav - u + \delta [I will call this (1)] du/dt = \betav - u [call this (2)] For what values of \beta and \delta are there no critical points? Homework Equations The Attempt at a Solution So...

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...

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...

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.

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...

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...

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...

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...

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...

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

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...

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...

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}}...

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

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...

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...

If yes, how can we find it?

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...

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?

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...

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...

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...

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}...

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 <...

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...

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...

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.

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...

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)...

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...

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 =...

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...

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...

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...

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...

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.

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?

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}...

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...

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...

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}...

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?

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

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...

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...

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

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...

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...

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...

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...