# 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.

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### How to define the light “color” from a given spectral distribution?

The following question may be naive and incomplete in some way I don't know. I'm not a specialist on spectroscopy, colours and light curves, color spaces, etc. Suppose you have a simple power-law ...
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### Statistical physics: How do I find the number of particles that have energy above/below a level?

Say I have a gas consist of atoms or molecules. How do I find the number of atoms in that ensemble that have energy above/below a specific amount, say E? I mean, what is the function that I'll have to ...
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### Why is the wave function inside a delta potential non-zero?

The wave function outside an infinite well is zero, owing to the fact that we assume particles to have finite energies. But in the case of a delta function potential $\delta(x-a)$, the wave function ...
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### Definitions of position operator in QM

We define the position operator $\hat{X}$ by $$\hat{X}|\psi\rangle := \bigg(\int dx |x \rangle x \langle x | \bigg) | \psi \rangle \tag{1}$$ for some state vector $| \psi \rangle \in \mathcal{H}$. ...
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### Questions About Quantum Delta Function Potentials [closed]

I didn't think that it would be possible for a wave function to get through the delta function because there is no "leakage" of the wave function through an infinite potential barrier. I can ...
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### How is the Dirac delta function used in classical mechanics? [closed]

If the contact force applied to a physical object (ex. empty bucket) is given by the Heaviside function: $$F(t) = F_0~H(t)=\begin{cases} 0, t<0 \\ F_0, t \geq 0\\ \end{cases}$$ Then,...
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### Practical way of expressing the $\delta$-function [closed]

I have got a problem in using the $\delta$-function. As we know, this function is often used to define a 'density'-related quantity. Such as the density of states or some correlation function. Take ...
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### How can we justify identifying the Dirac delta function with the eigenfunction of position? [duplicate]

I can think of at least two different ways to understand eigenfunctions of operators in quantum mechanics. But neither one seems to provide a good explanation for why we take the position-basis ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 v(R) = v_0, \tag{1} \end{...
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### 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 $\delta (x)$ ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...