# 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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### Maxwell Equations don't give unique Electric Field?

Consider the class of electric fields given by $$\mathbf{E}=\begin{cases} \ln (Cr)\hat{z} & 0\leq r < R\\ 0 & r> R \end{cases}$$ where $C$ is a constant and $r$ is the polar-distance ...
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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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### 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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### What does the Dirac delta function physically do while deriving Gauss Law form Coulomb's law?

While doing this derivation, the the source coordinates are mentioned as "$s$" and the coordinate of the point at which field is to be calculated is mentioned as "$r$". Kindly follow this Wikipedia ...
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### What is the charge density for line and surface charges?

In electrostatics it is common to see line, surface and volumetric charges being described differently. A line distribution is a function defined on the line, a surface charge distribution is a ...
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### Derivation of generation of time between two subsequent particle enters into computational domain

I have problem with understanding derivation of one equation in following problem. You have 1D computational domain (it is not 1D but because it is symmetrical and we are watching only radial ...
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### Derivation of Biot Savart law for a curve

I'm ok with the following expression for Biot-Savart: $${\mathbf B}({\mathbf r}) = \frac{{\mu _0}}{{4\pi }}\int\frac{{{\mathbf J}({\mathbf r'}) \times {(\mathbf{r-r'})}}}{{|\mathbf{r-r'}|^3 }}dV'.$$ ...
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The definition of "delta function normalization" says a basis of eigenfunctions of a particle in free space are orthonormal when $$\int_{-\infty}^{\infty}\phi_n^*(\vec{r})\phi_m(\vec{r})\mathrm{d}\vec{... 0answers 53 views ### How to calculate the second functional derivative of the action of a one-particle system? Given the Lagrangian$$L(q,\dot{q})=m\dot{q}^2/2-V(q)$$and the corresponding action$$S[q]\equiv\int_0^t dt' (m\dot{q}^2/2-V(q)),$$I need to be able to evaluate the second functional derivative \... 6answers 2k views ### What is the origin of the Dirac delta term in the dipole electric field? I am a bit lost how one has deduced the formula for electric field with electric dipole because of some inconsistency between different sources. The Wikipedia article contains a delta function in the ... 1answer 63 views ### Surface density charge, divergence of the electric field and gauss law ItÂ´s known that the divergence of the electric field at a certain point is given by this formula:$$\nabla \cdot E=\dfrac{\rho (r)}{\epsilon_{0}}$$Being \rho (r) the volume charge density at that ... 2answers 61 views ### Commutation Relations in Second Quantization I understand that if I have the field operators \psi(r) and \psi^\dagger(r), then I have the canonical commutation relation (in the boson case)$$[ \psi(r) , \psi^\dagger(r')]=\delta(r-r').$$My ... 1answer 51 views ### Book to study Dirac delta function from a physics point of view [duplicate] I am a beginning physics graduate student. I am often bewildered by the strange properties of the Dirac delta function such as: \delta (a x)= \frac{1}{a} \delta (x) The derivative of \delta (x) ... 1answer 268 views ### Imaginary Part of the Free Energy - Sohotski Plemenj theorem I have posted this question already on Math Stack Exchange and I hope not to annoy the community if I post it here again, looking maybe for a better suited audience. I need to understand how the ... 3answers 693 views ### Normalization of basis vectors with a continuous index? I have an infinite basis which associates with each point, x, on the x-axis, a basis vector |x\rangle such that the matrix of |x\rangle is full of zeroes and a one by the x^{\mathrm{th}} ... 0answers 38 views ### Why is the inner product of position eigenstates not normalised? [duplicate] I have read that$$<{\bf r}|{\bf r}'> = Î´({\bf r}-{\bf r}').$$I don't understand how this is correct, I want to say it is equal to 1 or 0, rather than an unnormalised delta function. Clearly ... 0answers 35 views ### graphical representation of Maxwell velocity distribution law I have read Maxwell's distribution law it is the probabilistic representation of no. Of particles having velocity between c to c+DC,through this representatation we can get the number of particle ... 3answers 199 views ### On the completeness relation in Quantum Mechanics Why does$$ \sum_n \Phi^{\ast}_n(x)\Phi_n(r)=\delta(xâˆ’r) $$represents a completeness relation? Or, put differently, why does it imply completeness? Is there any way to see it intuitively? Maybe an ... 1answer 89 views ### Delta functional in path integrals In a few articles dealing with path integral quantization I came across some calculations where apparently identities of the form \int (\mathcal{D}\Phi)\, \delta(-\partial_0\Phi+j)\,\,... 3answers 90 views ### Transition probability derivation I have encountered this limit while learning time dependent perturbation and transition probability in Sakurai. How to show this limit? I tried to integrate around x=0 but didn't get anything useful?... 1answer 87 views ### Operators, Distributions and States in QFT First of all, I will mention what I understand (pls. correct if wrong): States are vectors in the Hilbert space, to include continuous spectrum (and thus distributions), we expand this space to ... 0answers 60 views ### Representing propagators as Dirac delta functions [closed] I have found online, in particular on the wolfram site, http://mathworld.wolfram.com/DeltaFunction.html, certain identities that allow one to represent a delta function as limits. Of particular ... 2answers 418 views ### Normalized wave functions in position and momentum space Using the following expression for the Dirac delta function:$$\delta(k-k')=\frac{1}{2\pi}\int_{-\infty}^{\infty}e^{i(k-k')x}\mathrm{d}x$$show that if \Psi(x,t) is normalized at time t=0, ... 1answer 153 views ### In nonrelativistic Quantum Mechanics, is the expectation value of a sum of operators always equal to the sum of the expectation values? Suppose that \lvert \psi_n \rangle are the eigenvectors of a Hamiltonian, \hat{H}, which span some Hilbert space \mathcal{H} and satisfy$$\hat{H}\lvert \psi_n \rangle = E_n \lvert \psi_n \...
In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$ (cf. last formula on ...