Tagged Questions

87 views

Why is the integral of $\|\nabla f\|^2$ called the energy of $f$?

Let $\Omega$ be a region in $\mathbb{R}^2$ with $f:\Omega \to \mathbb{R}$ a smooth function. Why is the quantity, $$\tfrac{1}{2} \iint_{\Omega} \|\nabla f\|^2$$ Called the "energy" of $f$? I am ...
137 views

How to solve a time-dependent Schrodinger equation in periodic Dirac delta potential

I'm trying to solve a 1D time-dependent Schrodinger equation: $$i\frac{\partial \psi(x,t)}{\partial t}=\left[-\frac{1}{2} \frac{\partial^2}{\partial x^2}+V(x)+F(t)*x\right]\psi(x,t)$$ where $V(x)$ ...
93 views

numerical update rule for discretized hawkes excitation process

So I think I am just misunderstanding some simple notation or something and would appreciate some help. I am trying to replicate this model in an agent based model, but I cannot seem to figure out the ...
29 views

need to construct a function satisfying wave equation.

I need an example of a function that satisfies wave equation and that vanishes beyond certain range. I mean if $f(x,t)$ is a function of space and time, then $f(x, t) = 0,$ for $x < a(t)$ and ...
What is known about the solutions of the differential equation in three-dimensions $$\nabla^2 \phi = -\kappa^2 (\phi + (1/3!)\phi^3)$$ Without the cubic term, this gives a linear operator ...