Dirac Definition and 859 Threads

Would someone tell me some website where I can find the relativistic treatment of the hydrogen atom using Dirac's Equation? I am not trying the find the method which uses Schrodinger's equation and adds as perturbations fine and hyperfine structures? Thank you. So far i have not find anything...

hi how to calculate the traces of product of Dirac matrices in QED. i want caculate crossection of process scattering in QED. a program to calculate it

Homework Statement If D =7 and the metric g\mu\nu=diag(+------), Using the outer product of matrices, A \otimes B construct a suitable set of \gamma matrices from the 2 x 2 \sigma-matrices Homework Equations \sigma1=(0, 1 ) \sigma2=(0, -i)...

I don't understand in the first paragraph of the attached lecture notes. Could anyone help?

When I learned about Dirac's Equation, textbooks usually say that the earlier Klein-Gordon equation isn't linear in time derivative, contrary to what we expect from the time-dependent Schrodinger equation, therefore Dirac had to come up with a version that's linear. However, I think this doesn't...

Hello, It's well known that the action for a relativistic point particle is: S=-m\int d\tau\left(-\dot{x}^2\right)^{1/2} the canonical momentum is p_{\mu}= \frac{m\dot{x}_{\mu}}{\left(-\dot{x}^2\right)^{1/2}}. This action is invariant under reparametrizations of \tau, then its...

Homework Statement trying to simplify (using dirac notation) QM: <E| (QH - HQ) |E> using H|E> = E|E> Homework Equations The Attempt at a Solution the textbook says that it simplifies to (E-E) <E|Q|E> = 0 but i can't see how :S

Say we have, |\chi_3>=|a+ib> and we want : <\chi_3|H|\chi_3> is it correct to say: <\chi_3|H|\chi_3>= <a|H|a>+<a|H|ib>+<-ib|H|a>+<-ib|H|ib> ??

I am looking at a problem, part of which deals with expressing delta dirac as a limiting case of gaussian function. I am aware of the standard ways of doing it. In addition, I would also like to know if the following are correct - \delta(x-a) = \lim_{\sigma \rightarrow{0}} \int_{a -...

Hi, In a calculation I am doing, I encounter terms of the form \bar{u}^{s_1}(\boldsymbol{\vec{p}})\gamma^{\mu}{v}^{s_2}(\boldsymbol{\vec{q}}) where u and v are the electron and positron spinors. Is there any recipe for simplifying this expression, using the spin sums or other identities? I am...

Hello all. So I am trying to integrate a function of this form: \int\intF(x,y)\delta[a(Cos[x]-1)+b(Cos[y]+1)]dxdy The limits of integration for x and y are both [0,2Pi). I know that this integral is only nonzero for x=0, y=Pi. So this should really only sample one point of F(x,y)...

Hi, I'm working through Section 4-3 of Itzykzon and Zuber's QFT textbook, but I am a bit stuck while trying to understand some of the quantities and equations. First of all, what is this "one-body scattering operator \mathcal{F}(A)"? It is defined (eqn 4-89, page 188) as \mathcal{F}(A) =...

Hello, My question is about how dirac-delta function is derived by using this integral, \frac{1}{2\pi }\int_{-\infty}^{\infty}e^{ikx}dk=\delta (x) I couldn't solve this integral. Please help me. Thanks for all of your helps.

Studying the free electron model I found the fermi dirac distribution and the book told me that when T->0 we have that the fermi energy is equal to the chemical potential... why?

Hi, I find a lot of the time in QM i have been calculating things blindly. Take the expectation value for instance. I have worked this out in integral form plenty of times, but haven't really understood why I'm doing what I'm doing. I looked up wikipedia and apparently, for a measurable...

I was wondering if I integrate the dirac delta function from 0 to infinity where the function it's integrated with is the constant 1, will I get 0.5 or 1? And why? This is not homework so I decided to post this here although I asked this question in class and the teacher (assistant) wasn't...

Homework Statement I want to plot the following function into Maple14. \vec{v}=frac{1}{\vec{r^{2}}} \hat{r} **In case the latex is screwed this says v=r^(-2) *r-hat The Attempt at a Solution My code for Maple is the following, but it doesn't seem to work.restart; with(LinearAlgebra)...

[SOLVED] Proofs for Dirac delta function/distribution Homework Statement Prove that \delta(cx)=\frac{1}{|c|}\delta(x) Homework Equations \delta(x) is defined as \delta(x)=\left\{\stackrel{0 for x \neq 0}{\infty for x=0} It has the properties...

Hi Can somebody help me with this... Is is correct to say that, Integral(delta(0)) = 1 (limits are from -infinity to +infinity) I don't know latex and sorry for the inconvenience in readability. Thanks, VS

These problems are from Introductory Quantum Mechanics (Liboff, 4th Ed.) Note: I'm using "D" as the dirac delta function. 3.9 (a) Show that D( sqrt(x) ) = 0 This has me stumped. It is my understanding that the Dirac function is 0, everywhere, except at x=0. So, how can I show this to be...

i am now studying dirac equation and klein paradox if we confine to one dimension, we only need one alpha matrix, not three so in lower dimensions, maybe the dirac spinor is not of four components but fewer? i am curious about this question because it seems that as for the Klein...

Hi, I hope this is the right place to ask this Is it possible to expand the Dirac delta function in a power series? \delta(x)=\sum a_n x^n If so, what's the radius of convergence or how can I find it? Thanks.

Suppose I wind up with the relation f(x)\delta (x-x')=g(x)\delta (x-x') true for all x'. Can I safely conclude that f(x) = g(x) (for all x)? Or am I overlooking something? this is a little too close to dividing both sides by zero for comfort.

Homework Statement \int_{-\infty}^{\infty}{u(t)e^{-t}(\delta(t+1)+\delta(t-1))dt Homework Equations \int_{-\infty}^{t}{u(t)dt = \left\{\begin{array}{cc}0,&\mbox{ if } t< 0\\t, & \mbox{ if } t>0\end{array}\right. \int_{-\infty}^{\infty}{f(t)\delta(t-a)dt} = f(a) The...

Homework Statement 1. i need to obtain the result of x[n] * x[n] (convolution) where x[n] = δ[n] + δ[n-1] 2. I need to obtain the power of the signal x(t) = 4 cos (ω0t) + 2 sin (ω0t) + 2cos(4ω0t) for R = 1 k Ω Homework Equations 1.Who do you convolute 2 diracs ? 2. what is the correct...

I'm curious about the use of the Dirac Delta function. I am familiar with the function itself, but have never really seen in used in actual problems. The only problems I've worked with the function are those specifically about the function (ie. Evaluate the Dirac Delta function at x=3). My...

Where can i find the proof of dirac's function properties?

A B are two-body and one-body operators respectively. Is the following equation correct? If so, Would you give me the proof in real space? \sum\limits_{ijklm}\langle ij|A|km \rangle \langle m |B |l\rangle= \sum\limits_{ijkl}\langle ij|A B |k l\rangle

how do we apply dirac delta function?when do we apply?

Homework Statement Hi, I would like to know what is the right way to write continuous deltas standing in a circle of radius a? Homework Equations The Attempt at a Solution I am not sure weather it's δ(r-a) or is it δ(r-a)/|r-a| Thank you

Hi, I want to do the following calculation: c_{m,n} = \int_{-\infty}^{\infty} t^m \phi(t-n)\,dt I know three things: I know the values of c_{m,n} for m={0,1} and the first 4 for m={2,3} I know that my \phi is symmetric, i.e. \phi(t) = \phi(-t) The Fourier transform of \phi(t)...

Good book, The Strangest Man by Graham Farmelo a biography of Paul Dirac man into antimatter, not just physics but also generally how things were in the 1900`s including the wars and politics

Homework Statement The Identity to prove: Homework Equations Using Integration by parts The Attempt at a Solution I couldn't produce the denominator.

r(x) = x if x \geq 0 and r(x) = 0 if x<0 I have to show that: 1-\[ \int_{- \infty}^{+ \infty} r(x) \varphi ''(x) dx = \varphi(0) \] And 2- that the second derivative of r is the Dirac delta. And I managed to do this by integrating by parts. Howver, I don't get why I can't just write: \[...

Hi, i wonder somethin' when I see that definition of the matrice: \gamma^5=\gamma^0\gamma^1\gamma^2\gamma^3 I don't see why it is a pseudo-scalar.

I wonder if I can chose any 4x4 matrices \gamma^\mu which fullfil anticommutationn relations \{\gamma^\mu,\gamma^\nu \}=2g^{\mu\nu} as a matricies in Dirac equation: i \gamma^\mu \partial_\mu \psi= m \psi . What changes in the theory if I chose different matricies? (of course I have to...

Is it possible to incorporate into Dirac equation for proton the possibility of its transformation into neutron (isospin freedom)?

I wonder how Dirac equation transform under change of coordinates (in flat spacetime). Should I simply express partial derivaties of one coordinates in another or it is necessary to transform Dirac matrices as well?

If photon's cannot couple with other photons , then when we shoot photons through a double slit and we get an interference pattern , How are the photons interfering with the other photons , and if there is no such thing as half photon like the photon is either absorbed or it is not ...

Hi! I was taught that the dirac matrices are AT LEAST 4x4 matrices, so that means that I can find also matrices of higher dimensions. The question is: what do these higher-dimension-matrices represent? Are they just mathematical stuff or have they got a physical meaning? I ask that because in...

Hi, On p67 of shankar Principles of QM, he considers the delta functions derivative. He says: \int \delta'(x-x')f(x')dx'= \int \frac{d\delta(x-x')}{dx}f(x')dx'= \frac{d}{dx}\int \delta(x-x') f(x')dx'=\frac{df(x)}{dx} I don't understand how the second equality follows, how can the...

Dirac function :( Hello everyone... I have some triple with my PDEs course especially with the Dirac function. How can I prove it is discontinuous function? I do not know where can I start... Could somebody help me, please.

Homework Statement Show that \psi (\gamma^a\phi)=-(\gamma^a\phi)\psi Homework Equations Maybe \{\gamma^a, \gamma^b\}=\gamma^a\gamma^b+\gamma^b\gamma^a=2\eta^{ab}I Perhaps also: (\gamma^0)^{\dag}=\gamma^0 and (\gamma^i)^{\dag}=-(\gamma^i) The Attempt at a Solution The gammas are...

I guess the answer to this question actually should be pretty obvious, but I still have problems getting it right though. I wonder about the definition of the time ordered product for a pair of Dirac spinors. In all the books I've read it simply says: T\left\{\psi(x)\bar{\psi}(x')\right\} =...

if \phi is a angular coordinate , between (-\pi,\pi) ¿how much is \delta(\phi-\pi) with \phi=-\pi+\epsilon?

Can Dirac equation be used for many particles (fermions) system (i.e. a nucleus with many electrons)? And in this case how do you incorporate the anti-symmetry nature of the wavefunctions? Obviously Slater determined will complicate the equation to a point where it’s almost impossible to solve...

Hi! The Dirac delta satisfies \int dx f(x) \delta(x-a) = f(a) But how about \int d^3x f(x) \delta^{(4)}(x-a) Here, x and a are four-momenta, and the integral is over the regular 3-dim momentum. How does the delta behave here?

I have a question that is puzzling me as always...The Fermi-Dirac distribution function is (at T=0): f\epsilon=\frac{1}{e^{\beta(\epsilon-\epsilon_{F})}+1} and we know that we can subsitute f\epsilon by 1 for \epsilon< \epsilon_{F} and 0 otherwise. However what is f(-\epsilon)? The answer is...

The dirac equation for massless particles can be decoupled into separate equations for left and right handed parts. i \tilde{\sigma}^\mu\partial_\mu \psi_R= 0 and i \sigma^\mu\partial_\mu \psi_L= 0. Now we can have four solutions for each of the above equations. For the equation i...

Hi everyone, I uploaded a solution about Fourier transform. At the solution of this problem, it states that make convolution. But i tried to do convolution but my result is not same with this result. When you do the convolution with 2.10 and 2.11, is the result 2.13 correct ? How is it done ...