Dirac Definition and 859 Threads

There is many projection (or measurement) postulates in quantum mechanics axioms: von Neumann measurement, Luders postulate... But does anybody know sth. about DIRAC POSTULATE? Thx

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.

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)

There is a step that bothers me in my book (Ryder) on QFT and I can't seem to figure it out. It concerns the (spatial) rotation of the spatial part of the Dirac four current: \bar{\psi} \gamma \psi The crucial step here is \frac{1}{4}(\vec{\sigma} \cdot \vec{\theta})...

Question: Consider the motion of a particle of mass m in a 1D potential V(x) = \lambda \delta (x). For \lambda > 0 (repulsive potential), obtain the reflection R and transmission T coefficients. [Hint] Integrate the Schordinger equation from -\eta to \eta i.e. \Psi^{'}(x=\epsilon...

[FONT="Arial"][FONT="Arial"]Hello, What is the dirac delta function and how is it different from a probability distribution?

Suppose that we take the delta function \delta(x) and a function f(x). We know that \int_{-\infty}^{\infty} f(x)\delta(x-a)\,dx = f(a). However, does the following have any meaning? \int_{-\infty}^{\infty} f(x)\delta(x-a)\delta(x-b)dx, for some constants -\infty<a,b<\infty.

Let be the exponential: e^{inx}=cos(nx)+isin(nx) n\rightarrow \infty Using the definition (approximate ) for the delta function when n-->oo \delta (x) \sim \frac{sin(nx)}{\pi x} then differentiating.. \delta ' (x) \sim \frac{ncos(nx)}{\pi x}- \frac{\delta (x)}{\pi x}...

This isn't really homework, I'm just curious. So I'm dealing with the delta dirac function, and I was just wondering what would happen if we had two functions. So the sampling property, \int_{-\infty}^{\infty} f(t)\delta(t-a)\,\,dt = f(a) Now what if we had: \int_{-\infty}^{\infty}...

First, I need to be able to do equations in my post but it has been a long time since I posted here. Someone please point me to a resource that gives the how-to. If you make a infinitesimal rotation of the free-field Lagrangian for the Dirac equation, you get an extra term because the Dirac...

The following formula appears in P J Mulders's lecture notes http://www.nat.vu.nl/~mulders/QFT-0E.pdf {\cal C}~b(k,\lambda)~{\cal C}^{-1}~=~d(k,{\bar \lambda}) (8.18) where {\cal C} is charge conjugation operator. \lambda is helicity. I don't know why there is {\bar {\lambda}} on the...

bonjour from france, I thought that sum of dirac(x - xi)/g'(xi), where the xi verify g(xi) = 0, was a definition for dirac(g(x)). It was proposed, as an exercise, to prove the equality of the 2 terms. can one help me thanks ps : can i write this in latex?

Dirac Proves 0 = 1 Suppose A is an observable, i.e., a self-adjoint operator, with real eigenvalue a and normalized eigenket \left| a \right>. In other words, A \left| a \right> = a \left| a \right>, \hspace{.5 in} \left< a | a \right> = 1. Suppose further that A and B are canonically...

Delta Dirac - Question on my final :( :mad: Man I just had this final, and I didn't study the delta function enough. I totally bombed this question. I think I did ok on the rest of it... but I messed up bad on this question. I want to know the answer though. Solve the heat equation: u_t =...

I'm trying to linearize Klein-Gordon equation, following Dirac's nobel lecture: (E^2 - (pc)^2 - (mc^2)^2) \psi = 0 (E + \alpha pc + \beta mc^2) (E + \alpha pc - \beta mc^2) \psi = 0 Expanding the equations yields: -\alpha and \beta commutes with E and p -\alpha^2 = \beta^2 = 1 -\alpha...

Hi, After reading DJGriffiths sections on the DDF I have a question about evaluating it in regards Prob. 1.46 (a), to wit: "Write an expression for the electric charge density \rho(\vec{r}) of a point charge q at \vec{r}'. Make sure that the volume integral of \rho equals q." This is easily...

Let's discuss the Dirac equation in a gravitation field. I suggest to begin with the following article: http://arxiv.org/abs/math.DG/0603367" It is rather simple. Your comments would be helpful for me.

So there's something I don't quite understand. The density in the KG equation stands for charge density. Here are several questions: 1. For a KG particle, how do I (if it all) find the position probabilty density? 2. For a Dirac particle, what does the (now positive definite) density...

Just have a question about the dirac delta function. I understand how you would write it if you want to shift it but how would you scale it assuming we are using discrete time. Would you write 2*diracdelta[n] or diracdelta[2n]. Also, would that increase it or reduce it by 2 meaning that...

I've recently come across this function in one of my science classes and am wondering were this identity comes from: \displaystyle{\int{\delta(t-\tau)f(\tau)d\tau}=f(t)} Where \delta(t) is the dirac delta function and f(t) is any (continuous?) function.

How can I prove that no continuous function exists that satisfies the property of the dirac delta function? I thought it should be pretty easy, but it's actually giving me quite a hard time! I know that the integral of such a function must be 1, and that it must also be even (symmetric about the...

Hey everyone, a quick question: what is the Fourier space representation of the dirac delta function in minkowski space? It should be some integral over e^{ikx} (with some normalization with 2*pi's). I'm curious if the "kx" is a dot product in the minkowski or euclidean sense, and how one...

I'm trying to show that \int \delta \prime(x-x')f(x') dx = f\prime(x) can I differentiate delta with respect to x' instead (giving me a minus sign), and then integrate by parts and note that the delta function is zero at the boundaries? this will give me an integral involving f' and delta...

Hello, This problem is related to the beta decay of a neutron in a proton an electron and a anti-neutrino. I need to prove that, in the limit where the mass of the neutron and the proton goes to infinity, m_P, m_N \to \infty, we have \bar{u}\gamma^\mu(1-\alpha \gamma_5)(\gamma^\alpha k_\alpha...

I don't have pstricks...so I am going to use words. \text{contraction}\{ \overline{\psi}(x_1) \psi(x_1) \} My question: Propogators are usually dealing with different points...but what is the contraction of two quantities evaluated at the same point. Thanks.

I have a homework problem that asks me to interpret the two curves for when the Fermi level (Ef) is 0.25 eV. I ploted the two graphs and both of them look nothing alike when E < Ef. But both plots predict a probability of essentially zero when E > Ef. I was wondering why is there such a large...

If I had a function g(x) defined by g(x) = \int_{-\infty}^{\infty} f(x) \delta(x) dx where \delta(x) is the dirac delta function, what would dg(x)/dx be? The fundamental theorem of calculus requires that f(x) \delta(x) needs to be a continuous and differentiable function before I can...

I want to prove coulomb's low for a single charge point from the general form of coulomb's low: E→=1/(4∏€) ∫∫∫ ρv(ŕ) * (r→- ŕ→)/│(r→- ŕ→)│^3 dŕ using Dirac Delta function where r→ is the field point vector ŕ→ is the source point vector ρv(ŕ) is the volume charge density I really don't...

hello again, i have an integral to solve and not sure how to approach this: \int f(q+T)\delta (t-q)dq and the boundaries of integral are -inf +inf couldn't figure it out with latex. what I know about this is that if delta function is integrated like this, it would be just the value of...

I was unaware that one could obtain the Dirac equation as a result of a random walk. I believe that this has been done by other researchers, but I found it by Ord's papers: http://arxiv.org/find/quant-ph/1/au:+Ord_G/0/1/0/all/0/1 Anyone else find these interesting? My interest is due to...

just curiosity, if you integrate dirac-delta from exactly zero to infinity, will you get one or a-half? since it is symmetrical about zero, i think it is a half. is it? i mean: \int_{0}^{\infty} \delta(x) dx=\frac{1}{2} or is it 1? thanks.

Hello How to get the propagator for the Dirac equation (1+1) and forth and what about the Feynman's Checkerboard (or Chessboard) model Thanks I need Your help

Can someone help me understand the transition between these two steps? <x> = \iint \Phi^* (p',t) \delta (p - p') \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t) \right) dp' dp = <x> = \int \Phi^* (p,t) \left( - \frac{\hbar}{i} \frac{\partial}{\partial p} \Phi (p,t)...

i can't solve there problem, please help me 1) delta(y^2-a^2) = 1/absolute 2a[delta(y-a)+delta(y+a)] 2) f(y)delta(y-a) = f(a)delta(y-a)

NOTE: I actually found the correct answer while I was typing this :rolleyes: and since I already had it typed, I figured i would post anyway. mods you can do with it as you please or leave it for reference. thanks Here's the problem: A uniform beam of length L carries a concentrated...

1. INTRODUCTION Many students become frustrated when they first meet the Dirac Delta function, typically in a course involving electrostatics, or Laplace transforms. As it is commonly presented, the Dirac function seems totally meaningless: Either, it is "defined" as...

I have a test in Diff Eq. tommorow and part of the test is inovling the Dirac Delta function. I have no clue as to what it is at all. More specifically its Laplace and Inverse Laplace. If anyone could explain to me what the delta function is and how to use in in diff eq and what are its...

Sakurai credits B. L. van der Waerden 1932 a pretty derivation of Dirac equation from two-component wave functions. First decompose E^2-p^2=m^2 as (i \hbar {\partial \over \partial x_0} + {\bf \sigma} . i \hbar \nabla) (i \hbar {\partial \over \partial x_0} - {\bf \sigma} . i \hbar...

Can someone explain me the Dirac Delta function for the function: \vec A = \frac{\hat r}{r^2}

Hey there. In an exercise I was trying to show that every solution of the Dirac equation also solves the Klein-Gordon equation. Now I have two very simple questions: Is \gamma_\nu \gamma^\mu = \gamma^\nu \gamma_\mu ? And is \partial_\nu \partial^\mu = \partial^\nu \partial_\mu ...

Ok, I was given: Solve the following using superposition: \ddot{x}+2\dot{x}+4x=\delta(t) bounded by \dot{x}=0, x(0)=0 I solved the Homo eqn and got the following: x(t)=e^{-t}(\cos (\sqrt{3}t)+\frac{\sqrt{3}}{3}\sin ({\sqrt{3}t)) I also know that : \ddot{x}+2\dot{x}+4x=u(t)...

Hi all, I recently purchased Shankar's Principles of Quantum Mechanics which relies heavily on Dirac's bra-ket notation. I'm just wondering if this is the norm or should I get used to switching between what I'm learning and some other accepted standard notation? Thanks in advance!

Latex -- how to do Dirac slash notation How do you do Dirac slash notation using LaTeX? For instance, I want to be able to type /\partial = \gamma_i \partial^i /p = \gamma_i p^i /A = \gamma _i A^i with the slashes running through the symbols \partial , p, and A.

Consider the following state vector and Hamiltonian: |\psi (0) \rangle = \frac{1}{5}\left (\begin{array}{cc}3\\0\\4\end{array}\right ) \hat{H} = \left (\begin{array}{ccc}3&0&0\\0&0&5\\0&5&0\end{array}\right ) If we measure energy, what values can we obtain and with what probabilities...

let S be the Unit Step function for a function with a finite jump at t0 we have: (*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)] so: L{S'(t-k)}=s exp(-s k)/s-0-[1-0]*exp(-s k) = 0 & k>0 but S'(t-k)=deltadirac(t-k) and we know that L{deltadirac(t-k)}=exp(-s k) so...

Consider a particle in a harmonic pscillator potential V (x) is given by V = \frac{1}{2}m\omega^2 Also \hat a = n^\frac{1}{2}|n-1>, and \hat a\dagger = (n-1)^\frac{1}{2}|n-1> where \hat a = \frac{\beta}{\sqrt 2}(\hat x + \frac{i\hat p}{m\omega}) \hat a\dagger =...

How can I find the momentum density in the dirac field? Can someone show me, tell me how or give me a reference? Preferably not in relativistically covariant notation; I found this expression for the momentum density G, and want to know where it comes from...

Hi everyone, From the condition: \gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu} = 2g_{\mu\nu} how does one formally proceed to show that the objects \gamma_{\mu} must be 4x4 matrices? I unfortunately know very little about Clifford algebras, and for this special relativity project...