# Tagged Questions

The conditions on the edges of a domain when solving ordinary or partial differential equations.

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### Finding the odd parity bound state wave function for a particle in one dimension

Let a particle of mass $m$ and energy $E$ be moving on the $x$-axis in a potential $V(x)$ given by $$V(x)=\left\{\begin{matrix} -V_{0}, & -a<x<a\\ 0, & otherwise \end{matrix}\right.$$ ...
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### Boundary conditions for the heat equation when solving a mass density gradient

I'm working with a mass density gradient with length $L$ and I'm trying to solve the heat equation in 1-D (mass diffusion equation, $\partial_t\rho(t,x)=D\Delta\rho(t,x)$), but I'm not sure which ...
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### Sommerfeld radiation conditions for an electromagnetic field

There is some confusion in the definition of Sommerfeld radiation conditions for an electromagnetic field, which are related to the asymptotic behaviour of the field for a distance $r \to \infty$ ...
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### Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
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### Why are holomorphic boundary CFT2 primary operators massless in the AdS3 bulk?

I saw a claim in this paper that holomorphic boundary CFT$_2$ primary operators correspond to massless states in the AdS$_3$ bulk. Specifically, As always, we simplify the situation by assuming ...
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### Derivation of Boundary Conditions

Source: http://my.ece.ucsb.edu/York/Bobsclass/201C/Handouts/Chap1.pdf (page 6). I am trying to make sense of the derivation on the right side of these two integrals. The first one which says ...
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### An Electric Potential Glued to a Cubic Insulator to Replicate a Point Charge: Charge Distribution

I have been going back over this problem with a friend for the better part of a day: A potential is glued to a cube insulator so that outside of the insulator the field is the same as a point ...
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### Solving the 1-d time-independent Schroedinger's equation with an infinite boundary

In my introductory modern physics class we have examined time-independent solutions to the SchrÃ¶dinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles ...
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### Derivation of cylindrical line heat source problem?

I have a line heat source embedded inside a cylinder and I am trying to find the temperature distribution T(r,t). By using the similarity variable, the solution to the differential equation is ...
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### Can I apply symmetry to this boundary value problem (BVP)?

Let's say I have a hollow cylindrical shell with inner radius $a$ and outer radius $b$ and length $L$. The temperature at at z=L is $T_{2}$ and the temperature at z=0 is $T_{1}$. There is also an ...
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### Equivocal boundary conditions for Laplace equation of 2D “V”-shape conductor

A two dimensional infinite "V"-shape wedge conductor is earthed, wherein $\beta$ is the intersection angle. We can solve Laplace equation so as to get the electric potential inside the "V" zone, as is ...
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### Normal to the Hypersurfaces

I am trying to understand the derivation of the Hilbert-Einstein action. However it requires a knowledge about hyper-surfaces for the boundaries of the integrals and also about the normal to the ...
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### Is the system of equations of electrostatics underdetermined or overdetermined? [duplicate]

The following equations are equations of electrostatics: $$\nabla \times \vec E=0$$ $$\nabla\cdot\vec E=\dfrac{\rho}{\epsilon_0}.$$ These are 4 independent equations, while $\vec E$ has only 3 ...
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### Comparison of 1D and 3D wave functions

When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy ...
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### Axisymmetric fluid flow

I'm having trouble with a boundary condition. In a fluid mechanics problem, I have flow at $z = \infty$ flowing into a solid plate at $z = 0$ and then flowing radially, and the problem is given as ...
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### Physical interpretation of different boundary conditions for heat equation

When solving the heat equation, $$\partial_t u -\Delta u = f \text{ on } \Omega$$ what physical situations are represented by the following boundary conditions (on $\partial \Omega$)? $u=g$ ...
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### Behavior of the electric field on boundary surfaces

Consider this picture. Integrating over this infinitesimal box gives the following equivalencies: \int_{\Delta V} d^3r~{\rm div} \vec{E}(\vec{r}) = \int_{S(\Delta V)} d\vec{f} \cdot ...
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### Boundary conditions for Laplace's equation

Given a grounded conducting sphere, $V=0$ and $radius = R$, centered at the origin with a pure electric dipole (dipole moment $\vec p$) situated at the origin and pointing along the positive $z$ axis, ...
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### Boundary Condition for Perfect Conductor in Uniform Magnetic Field

When I was studying the perfect conductor scattering (Section 10.1) in Jackson's book, I was confused by the calculation for magnetic dipole induced by the incident wave. He simply said like "set the ...
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### Periodic boundary condition on a Wave Function of a Particle in a Box

Until now solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
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### Boundary conditions on wave equation

I am having trouble understanding the boundary conditions. From the solutions, the first is that $D_1(0, t) = D_2(0, t)$ because the rope can't break at the junction. The second is that ...
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### Computational Fluid Dynamics methods

I have read some articles about the finite difference method on a cartesian orthogonal grid. I understand how it works when Dirichlet boundary conditions are used, or when Neumann boundary conditions ...
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### equilibrium intensity Helmoltz equation

Helmoltz equation describes the evolution of the bulk electromagnetic field, even when doing scalar optics as an approximation. Beam Propagation Method is a common approximation that assumes certain ...
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### Why frequency and tension doesn't change in the two medium?

I am reading a book about wave mechanics. There are two different cord (one light and one heavy) connected together, one person waving the lighter one, the wave transverse to the right from the ...
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### Interface condition for heat exchange

I would like to compute the heat distribution of a piece of metal with some surrounding material. The heat is assumed to propagate by diffusion, so inside the metal piece and also on the outside, the ...
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### Greens function in EM with boundary conditions confusion

So I thought I was understanding Green's functions, but now I am unsure. I'll start by explaining (briefly) what I think I know then ask the question. Background Greens are a way of solving ...
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### What's the average position of oscillating particles in a box with periodic boundary conditions?

Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D). Now put a ...
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### Dirichlet and Neumann Boundary condition: physical example

Can anybody tell me some practical/physical example where we use Dirichlet and Neumann Boundary condition. Is it possible to use both conditions together at the same region? If we have a cylindrical ...
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### Help with the understanding of boundary conditions on $AdS_3$

So I am trying to reproduce results in this article, precisely the 3rd chapter 'Virasoro algebra for AdS$_3$'. I have the metric in this form: ...
Can Einstein's equations in vacuum $R_{ab} - \frac{1}{2}Rg_{ab} + \Lambda g_{ab}= 0$ be treated as a Dirichlet problem? I am thinking of something along those lines: Consider a compact manifold $M$ ...