# Questions tagged [dirac-delta-distributions]

Distributions are generalized functions, such as, e.g., the Dirac delta function. DO NOT USE THIS TAG for statistical probability distributions, profiles, graphs, plots, etc.

414 questions
Filter by
Sorted by
Tagged with
127 views

### Heisenberg EOM for $\langle x \rangle$ in momentum eigenstate - where is my error?

Equation of motion for expectation value of a quantum particle in a momentum eigenstate: $$\frac{d}{dt} \langle x \rangle = \frac{1}{i h} \langle [x,H] \rangle$$ and since it's in a momentum ...
417 views

2k views

### Surface density charge, divergence of the electric field and gauss law

It´s known that the divergence of the electric field at a certain point is given by this formula: $$\nabla \cdot E=\dfrac{\rho (r)}{\epsilon_{0}}$$ Being $\rho (r)$ the volume charge density at that ...
261 views

### Commutation Relations in Second Quantization

I understand that if I have the field operators $\psi(r)$ and $\psi^\dagger(r)$, then I have the canonical commutation relation (in the boson case) $$[ \psi(r) , \psi^\dagger(r')]=\delta(r-r').$$ My ...
263 views

### Potential of an axisymmetric disc with constant rotation velocity

I am having trouble understanding why the form of the 3D potential for a disc with a constant rotation velocity for circular orbits of stars within the disc \begin{equation} v(R) = v_0, \tag{1} \end{...
881 views

### Book to study Dirac delta function from a physics point of view [duplicate]

I am a beginning physics graduate student. I am often bewildered by the strange properties of the Dirac delta function such as: $\delta (a x)= \frac{1}{a} \delta (x)$ The derivative of $\delta (x)$ ...
43 views

### Why is the inner product of position eigenstates not normalised? [duplicate]

I have read that $$<{\bf r}|{\bf r}'> = δ({\bf r}-{\bf r}').$$ I don't understand how this is correct, I want to say it is equal to 1 or 0, rather than an unnormalised delta function. Clearly ...
267 views

### graphical representation of Maxwell velocity distribution law

I have read Maxwell's distribution law it is the probabilistic representation of no. Of particles having velocity between $c$ to $c+DC$,through this representatation we can get the number of particle ...
436 views

### Imaginary Part of the Free Energy - Sohotski Plemenj theorem

I have posted this question already on Math Stack Exchange and I hope not to annoy the community if I post it here again, looking maybe for a better suited audience. I need to understand how the ...
2k views

485 views

49 views

### The momentum representation of $x$ and $[x,p]$ [duplicate]

To deduce the momentum representation of $[x,p]$, we can see one paradom $$<p|[x,p]|p>=iℏ$$ $$<p|[x,p]|p>=<p|xp|p>−<p|px|p>=p<p|x|p>−p<p|x|p>=0$$ Why? If we ...
617 views

Beginning with the Schr\"odinger equation for $N$ particles in one dimension interacting via a $\delta$-function potential $$(-\sum_{1}^{N}\frac{\partial^2}{\partial x_i^2}+2c\sum_{<i,j>}\delta(... 1answer 218 views ### Dirac delta in field theory We start with a function$${\Delta(x) = \displaystyle \int \dfrac{d^3k}{(2\pi)^3 2k^0}}\left( e^{ik^\mu x_\mu} - e^{-ik^\mu x_\mu} \right).$$It is obvious to me that for t = 0 the above expression ... 0answers 138 views ### Problem in understanding Feynman's explanation of the Dirac-Delta function [duplicate] This is quoted from Feynman's Lectures' Normalization of the states in x: We return now to the discussion of the modifications of our basic equations which are required when we are dealing with a ... 1answer 213 views ### Interpretation of the Dirac-measure property First and foremost, apologies in advance for using an abuse of notation by placing the Dirac measure inside an integral. But given the circumstances, I have no choice. This is essentially a word by ... 3answers 3k views ### What really is a Dirac delta function? Yesterday a friend asked me what a Dirac delta function really is. I tried to explain it but eventually confused myself. It seems that a Dirac delta is defined as a function that satisfies these ... 2answers 3k views ### Normalized wave functions in position and momentum space Using the following expression for the Dirac delta function:$$\delta(k-k')=\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(k-k')x}\mathrm{d}x$$show that if \Psi(x,t) is normalized at time t=0, ... 1answer 1k views ### How to make rigorous the idea of a continuous complete set? In Quantum Mechanics, when using Dirac's formalism one of its features is the expansion of state vectors into continuous basis of eigenvectors of unbounded self-adjoint operators. Let \mathcal{H} be ... 2answers 2k views ### Definition of a line charge with Dirac delta function [closed] Is the following statement correct for a line charge distribution λ(x)?$$ρ(\mathbf r)=λ(x)δ(y)δ(z)$$If yes - what does it say? 1answer 1k views ### Dirac Delta in definition of Green function For a inhomogeneous differential equation of the following form$$\hat{L}u(x) = \rho(x) ,$$the general solution may be written in terms of the Green function,$$u(x) = \int dx' G(x;x')\rho(x'),$$... 1answer 393 views ### State time evolution of a quantum harmonic oscillator with a Dirac-Delta function as an initial state [closed] I have a question just like this Phys.SE problem here with a difference that our system is a harmonic oscillator (rather than a free particle). A particle with mass m is connected to a string with ... 2answers 3k views ### Gauss' law in differential form for a point charge I'm trying to understand how the integral form is derived from the differential form of Gauss' law. I have several issues: 1) The law states that  \nabla\cdot E=\frac{1}{\epsilon 0}\rho, but when ... 1answer 290 views ### How does one make sense of a delta function of a scalar field? Disclaimer: Originally posted on math SE, but thought that it was better in physics SE, so deleted my post on math SE and posted here. In the classic review summary of stochastic quantization here, ... 2answers 92 views ### Why don't both equivalent forms of this delta function give the correct answer? I am a bit confused on a basic problem involving a Dirac delta function being integrated over in a multiple integral. The original problem is to find the probability distribution in position-momentum ... 3answers 1k views ### Bound states of the V(x)=\pm \delta'^{(n)}(x) potential? The \delta(x) Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives \delta', \delta'', ... exist also, do they? If yes, can we look for ... 1answer 1k views ### Can operators be argument of Dirac Delta function In one part of Marc Bee's book on Quasielastic Neutron Scattering, he defines the pair correlation function$$ G(\textbf r,t) = \frac{1}{(2\pi)^3}\int I(\textbf Q,t)\text e^{-i\textbf Q.\textbf r}\ d^...
I'm studying scattering theory from Sakurai's book. In the first pages he gets to the following expression: \langle n|U_I(t, t_0)|i\rangle=\delta_{ni}-\frac{i}{\hbar}\langle n|V|i\rangle\int_{t_0}^...
Well, the idea is that I have a rod of length $L$ and force $F_0$. Now I have to distribute those $F_0$ Newtons on the rod. But the problem is, that I want to do it continuously. So what I want in the ...