# 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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### Matching conditions for perfect conductors in electro*dynamics*

I've been working through the problems on Wald's Advanced Classical Electromagnetism and recently I dealt with the scattering of a plane, circularly polarized wave off of a perfectly conducting ball (...
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### How do the fall-off conditions follow from the finiteness of the charge flux?

I'm reading Stromingers "Lectures on the Infrared Structure of Gravity and Gauge Theory". There, they want to derive fall-off conditions for the electromagnetic field strength tensor from ...
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### Stationary waves [closed]

Say we have a tube with one closed end and one open. Say that we have a hole at some point in the tube (not its half or a really specific height). The conditions which have to be imposed are that: we ...
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### Converting a first order quantized boundary condition to a second quantized boundary condition?

Background So there is a recipe to convert a First Quantised $\leftrightarrow$ Second Quantised Theory (we are following these Ashok Sen's Quantum Field Theory I of HRI institute's notes). ...
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### A contradiction in Nonrelativistic Quantum Field Theory

Reference : "Field Quantization" by W.Greiner & J.Reinhardt, Edition 1996. In the above reference as concerns the Hamilton density $\:\mathcal H\:$ and the Hamiltonian $\:H\:$ of the ...
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### String vibration under periodic boundry conditions

I wish to known which are the vibration modes (in case that they exist) of an string vibrating under periodical boundary conditions (PBC). The question is related to molecular dynamics simulations of ...
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### Coulomb gauge does not fix $\vec A$ uniquely. Is the solution to $\nabla^2{\vec A} = -\mu_0{\vec J}$ given in Griffiths unique?

With the Coulomb gauge $\nabla\cdot{\vec A}=0$, and $\nabla\times\vec A=\vec B$, the vector potential satisfies the Poisson's equation, $$\nabla^2{\vec A} = -\mu_0{\vec J},$$ which for $\vec J\to0$ ...
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### No slip boundary condition in Hele-Shaw Cell

A Hele-Shaw cell can be used to visualise potential flow around a cylinder. See this image from Van Dyke Album of fluid motion with the z axis of the cylinder pointing out of the page: Potential ...
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### What is the intuitive implication behind $L' = L + \frac{df}{dt}$ not affecting equations of motion?

I am referring to another post on the same question as this post: Lagrangian $L' = L + \frac{df}{dt}$ gives the same equations of motion In the first paragraph, the poster says: "It is well ...
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### Is there more than one GR action (if we include boundary terms)?

The action of GR is proportional to the Einstein-Hilbert action $$S_1=\int \sqrt{-g}R dx^4.$$ Now, $R$, contains terms of the form $\partial^2 g$. Using integration by parts, one can write this ...
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### Open boundary condition in hubbard model

In case of open boundary condition, crystal momentum is not a good quantum number anymore. I mean we can construct an $N×N$ matrix in position basis and diagonalize it to obtain the eigenvalues, but ...
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### Delta function: Intuitive way for boundary conditions

Giving the Schrödinger equation $$-\dfrac{\hbar^2}{2\,m}\,{\partial_x}^2\psi(x)+ V(x)\,\psi(x) = E\,\psi(x)$$ with potential $V(x) = V_0\,\delta(x)$. Solving this equation using an ordinary Ansatz ...
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### How does one apply the phase change of $π$ on reflection at the rigid end of a string?

Consider a string, with a free end $P$ and another end $Q$ which is rigidly fixed. Now, we start oscillating the point $P$ (with $0$ initial phase difference) and a wave starts traveling(in the ...
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### Boundary conditions for bulk partition function in AdS/CFT

In AdS/CFT, we are told that the bulk and boundary functions are equal: $$\tag{1}Z_{bulk}[J]= Z_{CFT}[J],$$ where on the left hand side of the equality, $J$ is interpreted as a boundary condition at ...
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### Constraining the metric on the boundary of space-time to get rid of unwanted equation of motion

I've posted this question on maths.stackexchange discussing the action I'm working with, which is (in Dirichlet boundary conditions) just the effective action of a minimally coupled free massive ...
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### Turbulent boundary layer: viscous sublayer definition

I have seen different definitions of the viscous sublayer within a turbulent boundary layer, through my searches. Ones say that the viscous sublayer area is for $y \leq 10 * \delta_v$ where $\delta_v$...
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### Euler-Lagrange solution of $L=\ddot{q}^2$?

I'm new to Calculus of variations and have a very basic question. Suppose we want to solve the Lagrangian $L=\ddot{q}^2$ using the Euler-Lagrange equation. My intuition tells me that the solution ...
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### Why does a ${\bf B}$-field follow a high $\mu$ core in an electromagnet?

I'm having a hard time trying to understand why ${\bf B}$-field lines tend to follow the path of a high $\mu$ material. Below is what actually happens when you apply a coil with some current around a ...
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### Contradiction in the boundary conditions for normal $\textbf{H}$-field

Consider the boundary between two magnetic materials with different relative permeabilities $\mu$. Using a small Gaussian pillbox at the surface and $\nabla \cdot \textbf{B} = 0$, we can show that ...
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### Periodic boundary condition (Born-Von Karman): does the size of the cube matter?

Periodic boundary conditions are chosen to faithfully represent the dynamical situation of electrons flowing through the metal. It's a better picture than the stationary wave one. We imagine a cube of ...
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### Neumann boundary condition on the radial Schrodinger equation

For central-potential problems in textbook quantum mechanics, the boundary condition is physically motivated. For finite-range potentials, we match to free-particle solutions (tunneling or scattering)....
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### Strings: Neumann and Dirichlet boundary conditions

As I understand it there are two possible boundary conditions for open strings. The Neumann boundary condition implies that the ends of an open string move freely with the velocity of light. The ...
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### Open strings and branes

In string theory, open strings are attached to branes. What does "attached" mean? Do they just interact with the branes, or are they related to them in some other way?
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### Is the momentum in the infinite square well observable or not?

I've read in posts such as this and this that the momentum operator is not self-adjoint in the infinite square well because the geometric space is a bounded region of $\mathbb R$, for example $[0,a]$ ...
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