# 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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### Delta function in Fermi's Golden rule [duplicate]

I am currently trying to understand the Fermi's golden rule. We consider a system with Hamiltonian: $$\hat H = \hat H_0 + \hat Ue^{i \omega t},$$ where the expectation value of $\hat U$ i much ...
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### Books about distribution theory? [duplicate]

I need tips on (elementary) books about distribution theory, with applications to physics and engineering. There is a one and a half page introduction (on page 910) to the Dirac delta function in ...
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### QFT and measures on distributions

Recently I came across the following slogan: ,,constructing quantum field theory on a space $X$ means constructing a measure on the space of all (Schwarz?) distributions $\mathcal{S}'(X)$''. I would ...
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### Green's function on torus

I have a question about the Green's function $G(z,w)$ on torus which takes the form (for example the first equation in the paper https://annals.math.princeton.edu/wp-content/uploads/annals-v172-n2-p03-...
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### Verify that the electrostatic potential satisfies the Poisson equation [closed]

I'm reading Sect1.7 of Jackson's classical electrodynamics but I have trouble following his argument. Could someone help explain how exactly the Laplacian is evaluated in 1.30? Is it calculated with ...
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### Coherent state basis of (relativistic) particle Fock space

For a neutral scalar bosonic particle of mass $m$, I consider a Fock space with an orthonormal basis of momenta eigenstates \begin{equation}\label{Fock-p-states} \left|p_1p_2\cdots p_n\right\rangle=\...
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### Do Equal Time Commutation / Anticommutation relations automatically also apply for spatial derivatives?

The question is basically in the title. My naive thought was that when a commutation relation holds for all field operators $\Psi(\vec{x})$ (by "all" I mean "at all positions $\vec{x}$") on a fixed ...
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### Limit of the $\sin^2$ function in the derivation of Fermi's golden rule

In the derivation of Fermi's golden rule one typically arrives at an expression of the form $$\frac{\sin^2(\omega t)}{\omega^2}$$ which is then converted to $$\pi t\delta(\omega).$$ I cannot ...
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### Rationalizing the current operator

In eq. 1.191 of Mahan Many-Particle Physics, the current operator is defined as $$j(r)=\frac{1}{2}\sum_ie_i[v_i\delta(r-r_i)+\delta(r-r_i)v_i].$$ I'm trying to make some sense of this definition. I ...
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### Double Sommerfeld Expansion

Consider the Fermi-Dirac expansion for an arbitrary function $f(\epsilon)$: $I(f)=\int_0^\infty d\epsilon\frac{f(\epsilon)}{e^{\beta(\epsilon-\mu)}+1}$ The large $\beta$ expansion of this quantity ...
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### Why Dirac delta function is considered as wave function?

I have read in my textbook that dirac delta function is regarded as wave function. But isn't it violating the condition required for a wave function ie . It becomes infinite $δ(x-x_0)$ at $x=x_0$ ...
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### Constraints in path integral and the Lagrange multiplier

I was reading some references on the slave-particle approach to the Kondo problem and Anderson model. It is known that the slave-particle is introduced in the large Hubbard $U$ limit of the system so ...
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### Colombeau Algebra for physics students

I have an undergraduate degree in physics, taken 2 years of calculus, and a rigorous course in linear algebra. I have not taken a math course in analysis, though have read a bit about it on my own. ...
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### Confusion regarding the bound state of a Delta-function potential and Tunneling

I was reading (Griffith's QM book) about the Bound states for delta-function potential of the form $-\alpha \, \delta(x)$ where $\alpha > 0$. I feel a bit conceptually unclear. Few doubts I have ...
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### Covariant form of Green's function for wave equation

In J. D. Jackson's "Classical Electrodynamics", page 614 in the 3rd edition, he states that you can write the Green's functions for the wave equation in covariant form using the fact that \begin{align*...
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### ${}$ Dirac delta potential

We know that the number of bound states for an attractive delta potential is one. If so what will the number of bound states for a particle in a repulsive delta potential? If $V(x)= +a \cdot \delta(x)$...
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### Deriving Current density of a Moving Point Charge Using the Continuity-Equation

Problem: We know, a point charge at position $\mathbf{r}_q$ has the charge density $$\rho_q(\mathbf{r})=q\delta(\mathbf{r}-\mathbf{r}_q) \tag{2}$$ if it moves with the velocity $\mathbf{v}$, we get ...
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### Interpretation of induced force between two Dirac delta potential wells

My question is based on MIT OCW course 8.04 problem set 6 question 5(e). https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/assignments/MIT8_04S13_ps6.pdf Consider two Dirac ...
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### Deriving the form of radial distribution function in molecular dynamic simulation?

I am trying to derive the equation 8.16 in the attached image from the definition of the radial distribution function. However, I am unable to derive it with proper constants of $\frac{2}{N(N-1)}$ My ...
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### Divergence of $\frac{ \hat {\bf r}}{r^2}$ , what is the 'paradox'?

I just started in Griffith's Introduction to electrodynamics and I stumbled upon the divergence of $\frac{ \hat r}{r^2}$ , now from the book, Griffiths says: Now what is the paradox, exactly? ...
### Writing a two variable function$f(x,t)$ in terms of Dirac-Delta $δ(x)$ function and a function $P(t)$?
How to write a two variable function $f(x,t)$ in terms of Dirac-Delta $\delta(x)$ function and a function $P(t)$? For example; I read something in a book. You can find the following picture. But ...