Dirac Definition and 900 Threads

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?

I am working through a problem relating to the conservation of probability in a continuity equation. However, I end up with a contradiction when trying to put the following into the Time-Dependent Schrodinger Equation \frac{\partial\psi(x)}{\partial t}=\frac{\partial\left\langle...

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...

Doesn't Agbonlahor look a lot like Paul Dirac? Mentalism

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...

If we consider nonrelativistic QM, we will find Galilean group under the hood. Thanks to this, group theory enables us to find equations of motion directly from the symmetry principles. For example, if we take only geometric symmetries, we will get that the state space is broken into irreducible...

Let's have a theory involving Dirac field \psi. This theory is decribed by some Lagrangian density \mathcal{L}(\psi,\partial_\mu\psi). Taking \psi as the canonical dynamical variable, its conjugate momentum is defined as \pi=\frac{\partial\mathcal{L}}{\partial(\partial_0\psi)} Than the...

Trying to solve the ODE mx''(t) + bx'(t) + kx(t) = F(t) with m measured in Kg, b in Kg/s and Kg/s^2, F(t) in Kgm/s^2 and x(t) in m with initial conditions x(0) = 0 and x'(0) = 0, i got the following Green's function G(t,t') = \frac{1}{m\omega} e^{-\omega_1(t-t')}\sinh\left[\omega(t-t')\right]...

OK, so my basic understanding of Dirac Delta Function is that it shows the probability of finding a point at (p,q) at time t. Dirac Delta is 0 everywhere except for (p_{0},q_{0}). So my question comes Is it possible that a point enters the (p_{0},q_{0}) and stays there (for some period of...

I have a question about the Dirac Equation. I know that if I have a given initial state in non-relativistic quantum mechanics, I can find the Fourier coefficients using that state, and then write down the wavefunction for any time. But if I have an initial state wavefunction (that is, the...

Does anyone know what the Dirac delta function would look like in a space with curvature and torsion? The Dirac delta function is a type of distribution. But that distribution might look differently in curved spacetime than in flat spacetime. I wonder what it would look like in curved spacetime...

Alright...so I've got a question about the convolution of a dirac delta function (or unit step). So, I know what my final answer is supposed to be but I cannot understand how to solve the last portion of it which involves the convolution of a dirac/unit step function. It looks like this: 10 *...

Alright, I'm in my first QM course right now, and one of the topics we've looked at is solving the one-dimensional time-independent Schrodinger equation for various potentials, such as the harmonic oscillators, infinite and finite square wells, free particles, and last, but not least, the dirac...

Homework Statement The function \delta(cosx) can be written as a sum of Dirac delta functions: \delta(cosx)=\sum_{n} a_{n}\delta(x-x_{n}) Find the range for n and the values for a_{n} and x_{n} The Attempt at a Solution Well, taking the integral of \delta(cosx), we only get spikes when...

The Dirac delta function, \delta (x) has the property that: (1) \int_{-\infty}^{+\infty} f(x) \delta (x) dx = f(0) Will this same effect happen for the following bounds on the integral: (2) \int_{0}^{+\infty} f(x) \delta (x) dx = f(0)...

Dirac equation and friends :) I was playing with Dirac equations and deriving some usefull details, Note sure for a calculation, is all the math right? Beginning: we require for a pure Lorentz trasf that the spinor field trasform linearly as: \psi'(x')=S(\Lambda)\psi(x)...

I have a line charge of length L and charge density /lambda on the Z-axis. I need to express the charge density in terms of the Dirac Delta function of theta and phi. How would I go about doing this?