# Questions tagged [differential-equations]

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### The reason why separation of variable works when solving laplace's equation in some cases

Given an appropriate situation, for example, a case where there are 2 grounded conductors (infinite sheet charges), one at $y=0$ and one at $y=a$, and a 3rd conductor (at $x=0$) perpendicular to both, ...
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### Lie symmetries of differential equation and ladder operators

There is literature on the lie symmetries of quantum harmonic oscillator differential equation. The generators satisfy certain lie algebra. On the other hand, we have ladder operator method. The ...
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### Reference to understand this branch cut question

I am currently reading a physics paper in which the authors have complexified an ordinary differential equation (ODE). They mention the following statement in the paper: "These branch points ...
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### Laplace equation for three semi-infinite conducting planes at potential V meet at the right angle to form a cubic corner

Let the planes be $x = 0$, $y = 0$ and $z = 0$ and they all have the same potential $V_0$. the question is to find the potential in the region $x > 0$, $y > 0$ and $z > 0$. I know that from ...
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### How does Kirchhoff's voltage law relate to the spatial derivative of voltage?

I'm reading this libretexts article on the basics of transmission line theory. In it, they include this circuit diagram as a model of a uniform transmission line: They then say that applying ...
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### How can I form an advection-diffusion SDE to obtain the desired discretization?

Suppose that $\mathbf{s}(t)\in S$ denotes the spatial location of a process at time $t$. Further, let $\mathbf{x}(\mathbf{s}(t))$ denote covariates at the location $\mathbf{s}(t)$. My goal is to write ...
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### Uniqueness of solutions of Maxwell equations [closed]

I have this exercise on my electromagnetism course : Consider that there exist two pairs of fields E and B that satisfy Maxwell's equations, with the same boundary conditions and have the same ...