# Tagged Questions

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.

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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### Distribute force over a rod

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 ...
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### Does regularity of distributions have anything to do with definiteness of their product?

Recently I've gone through some literature concerning causal perturbation theory (CPT). As is well known, it deals with UV divergences in QFT by defining products of (operator-valued) distributions ...
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### Where does this relativistic relation involving the delta function come from?

$$\int\delta(E^2-\mathbf{p}^2-m^2)dE=\frac{1}{2E_\mathbf{p}}$$ Shouldn't integrating the delta function like this just give 1?
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Let's have constraints for Yang-Mills theory: $$\varphi_{a} = \partial_{i}\pi^{i}_{a} - f_{abc}\pi^{b}_{i}A^{c}_{i}.$$ I have read the statement that $$\tag 1 [\varphi_{a}(\mathbf x), \varphi_{b}(\... 2answers 455 views ### What is the expectation value of the 3D delta function for the Hydrogen atom ground state? I'm trying to evaluate the expectation value of some perturbation Hamiltonian$$H=\alpha \delta^3(\vec{r}),$$where \alpha is a positive constant, for the ground state wavefunction of the hydrogen ... 1answer 101 views ### Dirac Notation Question Appearing In a Projection So I have a part of the energy eigenvalue equation that look like this:$$ \delta(\hat{x})|n\rangle Where n is the energy basis of the Hamiltonian I'm considering. To deal with this, I tried ... 2answers 2k views ### What is the square root of the Dirac Delta Function? What is the square root of the Dirac Delta Function? Is it defined for functional integrals? Can it be used to describe quantum wave functions? \begin{align} \int_{-\infty}^{\infty} f(x)\sqrt{\delta(... 1answer 638 views ### Mathematical interpretation of Poisson Brackets Lets say we are working in a classical scalar field theory and we have two functional  F[\phi, \pi](x) and G[\phi, \pi](x). In most of the references, starting with two functional the Poisson ... 1answer 149 views ### Fourier integral form of the delta function? I'm learning basic maths for physicist and was wondering what do we use the Dirac delta function for? What is the difference between "the Fourier integral form" and the usual way of expressing the ... 2answers 214 views ### Eigenstates of a Hermitian field operator Consider a Hermitian field operator \phi(x) with eigenstates satisfying \phi(x) |\alpha\rangle = \alpha(x) | \alpha \rangle  I'm trying to determine the inner product between the eigenstates. ...
I want to ask if it is reasonable that I use the Dirac-Delta function as an intial state ($\Psi (x,0)$) for the free particle wavefunction and interpret it such that I say that the particle is ...