Dirac Definition and 859 Threads

Previously I posted a question on the Dirac delta function and was informed it was not a true function, but rather a distribution. However, I have to admit I still did not understand why its integral (neg inf to pos inf) is unity. I've thought about this and came up with the following...

Homework Statement How do you show that int[delta(t)]dt from negative infinity to infinity is 1? Homework Equations Dirac delta function defined as infinity if t = 0, 0 otherwise The Attempt at a Solution My teacher said that it has to do with m->infinity for the following...

1. The problem statement Show that: \int_{-\infty}^{\infty} f(x) \delta^{(n)}(x-a) dx = (-1)^n f^{(n)}(a) The Attempt at a Solution I am trying to understand how to prove: \int_{-\infty}^{\infty} f(x) \delta '(x) dx =- f'(x) I know that we need to use integration by parts, but I'm...

ψ(x) is the four-component wave function of the Dirac equation，that is ψ(x) can be expressed by a column vector (ψ1(x) ψ2(x) ψ3(x) ψ4(x)） ,under a lorentz transformation,it will become ψ'(x').I am confused that how ψ'(x') can be expressd in the form which is stated by textbooks: ψ'(x')=S(a)ψ(x)...

Griffiths' section 1.5.3 states that the divergence of the vector function r/r^2 = 4*Pi*δ^3(r). Can someone show me how this is derived and what it means physically? Thanks in advance.

Homework Statement Starting with the definition of the Dirac delta function, show that \delta( \sqrt{x}) um... i have looked in my book and looked online for a problem like this and i really have no clue where to start. the only time i have used the dirac delta function is in an integral...

Hi, if I want to calculate the generating functional for the free Dirac Field, I have to evaluate a general Gaussian Grassmann integral. The Matrix in the argument of the exponential function is (according to a book) given by: I don't understand the comment with the minus-sign and the...

Hi I have been trying to learn dirac delta function. but its kind of confusing. I come across 2 contrasting definitions for it. The first one states that the function delta(x-xo) is infinite at x=x0 while the other states that delta(x-x0) tends to infinite as x tends to x0. Now both of them...

Hi, I have learned the Dirac equation recently and I managed to solve it for a free particle (following Greiner book “relativistic quantum mechanics” and Paul Strange book “Relativistic Quantum Mechanics”). I was asked to solve the Dirac equation in the stationary frame for a free particle (no...

Some confusions from some recent lectures; I asked the prof, but I still don't fully understand what is going on. We began with the action (tau is some worldline parameter, dots indicate tau derivatives; they are hard to see): S = \int d\tau \; \left\{ \dot x^{\mu} p_{\mu} - \frac12 e(\tau)...

Hey there! I'm faced with this problem: http://img7.imageshack.us/img7/4381/25686658nz9.png It's a 1D nonhomogeneous wave equation with a "right hand side" equaling to the dirac delta function in x * a sinusoidal function in t. I have to find its general solution with the constraints...

Hello everyone, I'm not sure if these questions are really trivial or of they're a little subtle... but here goes. 1. In Ramond's text (Field Theory: A Modern Primer), he explains that the Lagrangian for fermions should have the derivative operator antisymmetrized in order for the kinetic...

By definition of the Dirac delta function, we have: \int f(x) \delta(x-a) dx=f(a) This is fair enough. But in ym notes there is a step that goes like the following: \mathbf{\nabla} \wedge \mathbf{B}(\mathbf{r})=-\frac{\mu_0}{4 \pi} \int_V dV'...

I cannot get the answer as from the solution manuel. Please tell me what am I assuming wrong. Thanks

I'm posting this here because I'm asking about the mathematical properties of the Dirac delta function, delta(x) which is zero for all non-zero real values of x and infinite when x is zero. The integral (-inf to +inf) of this function is said to be 1. How is this derived?

Can anyone explain what's negative energy mean in Dirac theory? Does it imply anti-particle travel backward in time?

Homework Statement Hi there, i am trying to do a proof that H'(t)= δ(t) Homework Equations We have been given the following: F is a smooth function such that lim (t-->±∞)F(t)=0 Therefore the integral between ±∞ of [H(t)F(t)]'=[H(t)F(t)]∞-∞=0 I understand it up until this point...

I think that anyone who has done a course in QFT has had their progress hampered by AT LEAST a month by Dirac Spinors. Why is it that the only sensible way to write the Standard Model down is to use Weyl Spinors, but the only sensible way to do calculations is to use Dirac spinors and...

The http://en.wikipedia.org/wiki/Dirac_equation" , which itself is based upon the relativistic energy-momentum relation E^2 = p^2 + m^2 (natural units). And here comes my question then: Why do we throw away the negative energy solutions in relativity but do we keep them when we combine it...

URGENT: QM Series Representation of Bras, Dirac Brackets Homework Statement Suppose the kets |n> form a complete orthonormal set. Let |s> and |s'> be two arbitrary kets, with representation |s> = \sum c_n|n> |s'> = \sum c'_n|n> Let A be the operator A = |s'><s| a) Give the...

Hi, I have a question about using the dirac function in a double integral. Lets say you have the double integral over the two values x1 and x2: int( int( sin(x1) * dirac(x1-x2) * sin(x2) )) Does this just simplify to a single integral: int( (sin(x1))^2 ) thanks!

Homework Statement I'm given the eigenvalue equations L^{2}|\ell,m> = h^2\ell(\ell + 1)|\ell,m> L_z|\ell,m> = m|\ell L_{\stackrel{+}{-}}|\ell,m> = h\sqrt{(\ell \stackrel{-}{+} m)(\ell \stackrel{+}{-} m + 1)}|\ell, m \stackrel{+}{-} 1> Compute <L_{x}>. Homework Equations Know...

I have recently finished reading a section on this notation, and while i though i understood it, i now find myself lost The question is to show that <m|x|n> Is zero unless m = n + or - 1 As I understand it so far <m| and |n> correspond to the eigenstates of an arbitrary system and x...

During my research a while ago, I have unexpectedly derived a "modified Dirac equation" with a \gamma_{5} mass term. (\gamma^{\mu}\partial_{\mu}+\gamma^{5}m)\psi(x)=0 I was quite surprised, and went about asking a few people. The answer I got is this equation is not new and has been...

Hi. Recently day, I tried to solve quantum mechanics problem in liboff fourth version to prepare graduate school. But what make me be confused a lot is Dirac Delta Function. One of my confusing on Dirac Delta is what i wrote below. -One of the formula describing Dira Delta...

Can anybody suggest me the link where i can prove "IN DIRAC THEORY FREE PATICLE POSESS ACCELERATION

Homework Statement Hi all, how i can prove that in dirac theory free particle possesses acceleration. Homework Equations The Attempt at a Solution Did not find anywhere.

hello every body i am a new M.S student and i can't understand the Dirac delta function can anyone simply describe it to me in order to simplify it. thank you

Hi. I came across a problem in a book of mine that requires me to find the dual of a vector |x> = A |a> + B |b>. However, it's a bit sketchy about taking |x> to <x|. With a little algebra, I got |x>i = A |a>i + B |b>i So <x|i = |x>i* = (A |a>i + B |b>i)* = (A |a>i)* + (B |b>i)* = A*...

Find a distribution F in R^2 that satisfies (Dx) F(x,t) = t*Delta(x) It is apperantly not t*H(x) as in R. * is multiplication, D is dirac delta, H is Heavyside , (Dx) is derivation with respect to x (in the sense of distributions) Sorry for not using Latex. Indeed I am trying to...

Derivative Using Dirac Delta Function Homework Statement Let \theta(x) be the step function: \theta(x) be equivalent to 1, if x > 0 0, if x \leq 0 Show that \frac{d \theta }{dx} = \delta(x) Homework Equations In the previous portion I was able to prove x \frac{d}{dx}...

Show that \stackrel{lim}{\alpha \rightarrow \infty} \int^{\infty}_{-\infty}g(x)\sqrt{\frac{\alpha}{\pi}}e^{-\alpha x^2} dx = g(0) where g(x) is continuous. To use the continuity of g(x) I started from \left|g(x)-g(0)\right|<\epsilon and tried to put it in into the integral...

see the attachment please answer

Hi I'm curious, how did the dirac equation predict the existence of anti matter? what was the mechanism that made physicists believe it existed? Thank you

Given: f(x)=\delta(x-a) Other than the standard definitions where f(x) equals zero everywhere except at a, where it's infinity, and that: \int_{-\infty}^{\infty} g(x)\delta(x-a)\,dx=g(a) Is there some kind of other definition involving exponentials, like: \int...

Homework Statement Three-dimensional particle is placed in a Dirac delta potential: V = -aV_{0}\delta(r-a) Find energy states and eigenfunctions for the angular quantum number l = 0.[/ Homework Equations The Attempt at a Solution It's not clear to me what boundary...

Three-dimensional particle is placed in a Dirac delta potential: V = -aV_{0}\delta(r-a) Find energy states and eigenfunctions for the angular quantum number l = 0.

Hey I was hoping you guys could clarify some stuff in Dirac, I'm trying to sort through the Schrodinger representation: 1) What exactly is the standard ket > ? Can anyone give me it in terms of pure linear algebra? What does it mean for it to be unity in terms of wave functions?? 2) I...

Hi, I need your help with a very standard proof, I'll be happy if you give me some detailed outline - the necessary steps I must follow with some extra clues so that I'm not lost the moment I start - and I'll hopefully finish it myself. I am disappointed that I can't proof this all by myself...

Homework Statement Find the bound state energy for a particle in a Dirac delta function potential. Homework Equations \newcommand{\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } } - \frac{\hbar^2}{2 m} \ \pd{\psi}{x}{2} - \alpha \delta (x) \psi (x) = E\psi (x) where \alpha >...

How does one calculate the number of components a Dirac spinor in arbitrary dimensions? As far as I understand, the textbooks treat the four spacetime dimensions and here the spinor has four components because the gamma matrices must be 4x4 in nature to satisfy the required algebra. Now suppose...

I'm stuck on a problem. Given a Hamiltonian [tex] H_{ab} = cP_j(\alpha^{j})_{ab} + mc^{2} (\beta)_{ab} [/itex] then [tex] (H^{2})_{ab} = (\textbf{P}^{2}c^{2} + m^{2}c^{4}) \delta_{ab} [/itex] holds if [tex] \left\{\alpha^j,\alpha^k}\right\}_{ab} = 2 \delta^{jk} \delta_{ab} [/itex]...

When Dirac solved his equation for electron, he found out there are negative energy states. My question is why electrons won't jump from positive energy state to negative energy states and release energy as photon? Dirac proposed that all negative energy states have been filled so electrons...

So I am trying to derive the continuity equation: \frac{\partial}{\partial x^{\mu}}J^{\mu} = 0 From the Dirac equation: i\gamma^{\mu} \frac{\partial}{\partial x^{\mu}}\Psi - \mu\Psi = 0 And its Hermitian adjoint: i\frac{\partial}{\partial x^{\mu}}\overline{\Psi}\gamma^{\mu} -...

[SOLVED] Dirac delta function Homework Statement Prove that \delta(cx)=\frac{1}{|c|}\delta(x) Homework Equations The Attempt at a Solution For any function f(x), \int_{-\infty}^{\infty}f(x)\delta(cx) dx = \frac{1}{c}\int_{-\infty}^{\infty}f(t/c)\delta(t) dt where I have...

This is probably a silly question to some, but I've been struggling to understand how the delta function behaves when given a complex argument, that is \delta(z), z \in C. I guess the basic definition is the same that the integral over all space is 1, but I'm looking for a more detailed guide on...

[SOLVED] Dirac delta function and Heaviside step function In Levine's Quantum Chemistry textbook the Heaviside step function is defined as: H(x-a)=1,x>a H(x-a)=0,x<a H(x-a)=\frac{1}{2},x=a Dirac delta function is: \delta (x-a)=dH(x-a) / dx Now, the integral: \int...

I am studying for a Quantum Mechanics final and our prof. gave us an equations sheet with some of the equations needed for the exam. I was wondering what the following equations could be used for. We have covered spherical harmonics, the Hydrogen Atom, Degenerate Perturbation Theory, Spin...

[SOLVED] Fermi Dirac- missing something from Ashcroft derivation Homework Statement Deriving Fermi Dirac function following ashcroft all good up to equation 2.43 but then it does the folowing at 2.44 and I can't see how you reach 2.44. Homework Equations as (2.43) f_{i}^{N}= 1-...

According to the principle of general covariance, the form of equations should be independent of the coordinates chosen. In general relativity, this is implemented by expressing laws of physics as tensor equations. In physics equations are often expressed in index notation, which allows...