# 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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### Derivation of the wave field from an impulsive planar source

The figure shows the geometry for deriving the wave field from an impulsive planar source. The impulse is approximated by a rectangle $c\epsilon$ wide and $\alpha=\frac{1}{c\epsilon}$ high so the ...
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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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### Towards a matrix element definition of PDF

In Schwartz's book, 'Quantum Field Theory and the Standard Model' P.$696$, he starts to derive an expression for a parton distribution function in terms of matrix elements evaluated on the lightcone. ...
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### Delta potential in terms of annihilation/creation operators

Let the Hamiltonian of a system on a discrete lattice be given by $$\mathcal{H} = \gamma \sum_\vec{x} c^\dagger_\vec{x}c^\vphantom{\dagger}_{\vec{x}+\vec{y}} + \text{h.c.},$$ where $\gamma$ is ...
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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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### 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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### 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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### ${}$ 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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### Integration over phase space for a one-dimensional harmonic oscillator

The problem asks for a proof of the following equation, and I have no idea on how to approach this: $$\int dx dp \delta(E-\frac{p^2}{2m}-\frac{m \omega^2 x^2}{2})f(E) = \frac{2\pi}{\omega}f(E) ,$$ ...
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### Quantum filter, potential barrier

I have been trying to teach myself quantum mechanics for quite a time now and I need help with a probably simple problem. We are looking at the Schrödinger equation of particles of mass $m$ in one ...
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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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