# Questions tagged [boundary-conditions]

This tag is for questions regarding to the boundary conditions (b.c.) which expresses the behaviour of a function on the boundary (border) of its area of definition. The choice of the b.c. is fundamental for the resolution of the computational problem: a bad imposition of b.c. may lead to the divergence of the solution or to the convergence to a wrong solution.

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### Existence of Green's functions with specific causality conditions

This is a follow-up to my previous question here: Green's identity for arbitrary differential operators. Given some scalar field theory with field $\psi$ and source $\rho$ with field equations \...
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### Green's identity for arbitrary differential operators

If we have a scalar field $\psi$ that satisfies an equation $\nabla^\mu \nabla_\mu \psi = \rho$ where $\rho$ is some known source we can use Green's identity to express it as \begin{equation} \psi (x)...
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### About the usage of the Green's function

This question is very basic, but I'm a little confused about this topic (I "learned" it during my bachelor's degree but never used it before). I have an electrostatic problem described by ...
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### Diffuse boundary condition for fermigas/bosongas

I'm doing math, usually working only in the classical framework, but my background in quantum physics is close to zero so please forgive me if the question does not make sense. I was looking into ...
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### How many boundary conditions do we need to solve Laplace's equation?

I'm struggling to understand which boundary conditions are necessary to solve Laplace's equation. In order to better understand them, I have thought of a scenario that I would like to ask a couple of ...
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### Finding the potential of a point charge and a conductive sphere solving Laplace's equation

How can we solve this, specifically using the method of separation of variables, instead of the method of the images? Specifically, outside the sphere We have a conductive sphere of radius R at the ...
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### Temporal Gauge with periodic boundary conditions

In Yang-Mills theory with periodic boundary conditions in time, is the temporale gauge, i.e. $A_0 = 0$, well defined? Periodic boundary conditions would be $$A_\mu(T_2,x) = A_\mu(T_1,x).$$ Naively I ...
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### The WKB approximation and boundary conditions

To estimate a quantization rule using the WKB approximation, one is usually working in the 'classically allowed region'. You apply the WKB approx in the middle of the region and use the Airy ...
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### Legendre series solutions for the Laplace equation: can Neumann boundary conditions be applied?

In Jackson E&M, it is shown in equation (3.33) that the Laplace equation with azimuthal symmetry can be expanded in Legendre series in spherical coordinates,  \Phi(r,\theta)=\sum_{l=0}^\infty\ [...
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### QED photon path (direction of photon emission)

In QED we look at all possible path a photon could go from S to P, and I understand the most significant contributions to the final arrow are the few near straight paths connecting S and P while other ...
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### How to solve dual boundary condition contradiction at the corner of an axially loaded cylinder?

Subject: Linear elasticity Consider an isotropic elastic cylinder rigidly bound to the surface on one end. The other end is under uniformly distributed static load (pressure for example). I am trying ...
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### Surface charge density on an open conductor

In Griffiths' "Introduction to electrodynamics" (3rd edition, page 102) he states that: since the electric field inside a conductor is zero, boudary condition 2.33 (\$\mathbf{E_{above}-E_{...