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Questions tagged [boundary-conditions]

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1answer
32 views

Physical meaning of impulsive boundary condtion [closed]

In this paper, the author study a wave motion initiated by a delta at the interface of two media. A model problem is : $$ \partial_{tt}^2\, u(t,x,y) = c^2_+ \Delta u(t,x,y) \quad \text{in}\; x>0,...
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1answer
30 views

Clarification of this statement on image charges?

I am currently studying the uniqueness theorems and their applications in electrostatics. I then came across a problem which mentions: "The standard electrical image method fails because the image ...
2
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1answer
80 views

Boundary conditions for the numerical particle in a box example

I want to solve the one-dimensional Schrödinger equation for the particle in a box example, and want to force the wavefunctions to zero on the boundaries. I am using the matrix, \begin{equation} \hat{...
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0answers
48 views

What are the boundary conditions for D4-branes ending on D8-branes?

In a recent paper by Cordova and Jafferis, they perform the physical derivation of the AGT correspondence. A crucial step is recognizing that the appropriate boundary conditions for the 5D super Yang-...
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2answers
195 views

Does the quantization come from that the wave function $\psi$ should vanish at infinity?

For one dimensional non-relativistic quantum mechanics, the solutions to $\hat H\psi=E\psi$ seems not requiring the energy $E_n$ to contain the "$n$" term without specific boundary conditions. Does ...
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0answers
52 views

Why boundary conditions of an open string involve the time derivative?

I am trying to understand the boundary conditions of an open string stretching from one brane to another, in TIIA theory. Let's consider to D6-branes which spans a line along the $(x_4,x_5)$ plane ...
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1answer
368 views

The derivation of the Planck distribution

I am trying to understand the Planck distribution and black body radiation. In the Wikipedia derivation of the Planck distribution, the photons confined within a cubic box, are emitting from and ...
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2answers
117 views

Continuity of tension in falling objects

Imagine I'm holding a block of mass $m_1$. At the bottom of this block is a rope that is fastened to another block of mass $m_2$. We're in a uniform gravitational field $g$. In a minute I'm going to ...
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1answer
370 views

Boundary conditions on radial Schrodinger equation for $V(r)=A/r²-B/r$ potential

I have to solve the radial Schrodinger equation for a particle subjected to the potential: $$V(r)= \dfrac{A}{r^2}-\dfrac{B}{r}$$ Where $r$ is the radial component (spherical coordinates) and $A,B&...
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0answers
41 views

What is happening physically when we vary the $\alpha$ in the impedance boundary condition $u + \alpha \frac{\partial u}{\partial n} = 0$?

Say are considering acoustic waves in a domain $D$ filled with water and with an impedance boundary condition $$ u + \alpha \frac{\partial u}{\partial n} = 0, \quad x \in \partial D, $$ where $\alpha ...
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1answer
52 views

Why does $\delta g^{\mu\nu}=0$ on a boundary imply that the tangential derivative of $\delta g^{\mu\nu}=0$ too?

In https://arxiv.org/abs/0809.4033, between Eq. (4.2) and (4.3), the authors state that setting $\delta g^{\mu\nu}=0$ on a boundary implies that the tangential derivative $h^{\alpha\beta}\partial_\...
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1answer
77 views

The average of inverse square radius $r^{-2}$ for any state quantum $|n\ell\rangle$ using the radial Schrödinger equation [closed]

I have a problem understanding the solution provided for the problem here: It's from the book "Quantum Mechanics - Concepts and Applications", 2nd ed., by N. Zettili (Wiley, 2009). My issue is that ...
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2answers
312 views

What is the boundary condition for Ginzburg Landau equation?

I am trying to do some numerical calculation with Ginzburg-Landau (GL) equation for a superconductor. However, I am confused about the boundary condition of the GL equation. If we introduce the GL ...
2
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1answer
81 views

Boundary conditions due to local and global diffeomorphisms

Consider the following extract from page 2 of this paper. $AdS_3$ is the $SL(2, \mathbb{R})$ group manifold and accordingly has an $SL(2, \mathbb{R})_{L} \times SL(2, \mathbb{R})_{R}$ isometry ...
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0answers
57 views

Topological insulators: What does the scattering matrix at an topological edge tell about the Chern number?

In class we were briefly discussing, that one way to see if the edge of a TI carries a state is to consider the scattering of a lead that is attached to this edge. In fact the argument was more ...
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1answer
209 views

Neumann or Dirichlet boundary conditions?

I'm working on a question here where I have solved these boundary conditions; $$\vec{n} \cdot \vec{j}= -\lambda\vec{n} \cdot \nabla u + k(\rho - \rho_0)u\vec{n}\cdot\vec{g}=0$$ So my question is, ...
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1answer
129 views

A question on the formulation of core-shell quantum dot Boundary conditions in K.P method

When studying the energy levels of core-shell quantum dots with eight-band k.p method, an important part is the formulation of boundary conditions for wavefunctions. In the Supporting Information of ...
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2answers
3k views

Periodic boundary condition for a particle in a box

I've been trying to solve the Schrödinger equation for a particle in a box of volume $V$ (length $L$) with periodic boundary conditions. The general solution for the equation yields, for one dimension,...
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0answers
85 views

Power in a wind turbine

An wind turbine starts turning by a wind speed of $v_b$ and it stops turning (rated wind speed, to prevent overloading) by a wind speed of $v_g$. By wind speeds between $v_b<v<v_g$, the power ...
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5answers
4k views

Normalizable wavefunction that does not vanish at infinity

I was recently reading Griffiths' Introduction to Quantum Mechanics, and I stuck upon a following sentence: but $\Psi$ must go to zero as $x$ goes to $\pm\infty$ - otherwise the wave function would ...
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1answer
646 views

Boundary conditions in fluid dynamics

I have been working on some questions and have noticed that my main problem is with finding boundary conditions for problems in fluid dynamics which involve oscillations. The two questions in ...
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0answers
37 views

Boundary conditions for a complicated diffusion equation problem

this is my first post/question, so any constructive criticism on how to ask questions better is also welcome I have this problem: we have an infinite(in z axis) cylindrical tube, from $R1$ to $R2$ ...
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0answers
30 views

How can wave propagation in a solid-fluid problem be modelled, and in particular how are transmission boundary conditions handled?

When dealing with wave propagation problems such as electromagnetic waves passing from one medium to another we set up boundary conditions to ensure the field is continuous and the flux is continuous ...
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2answers
819 views

Necessity of the Gibbons-Hawking-York (GHY) boundary term

The fundamental point of my question is whether the GHY-boundary term in general relativity is even necessary at all, and if yes, then why is it so, and what is its physical significance. Several ...
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1answer
52 views

What am I doing wrong when applying boundary conditions in this E&M problem?

I don't understand boundary conditions very well yet, it would seem. I'm sure this is very simple. In analyzing a situation where a monochromatic plane wave approaches an interface (with polarization ...
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2answers
371 views

Boundary condition in a real conductor

The boundary condition $\textbf{n}\times \textbf{H}=\textbf{K}$ (A/m) is valid in the surface of a perfect conductor (where the conductivity $\sigma$ is infinity). Is it satisfied for the surface of a ...
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2answers
277 views

Justification for acoustic wave equation boundary conditions

In analyzing the standing acoustic waves produced by a wind instrument, one usually assumes that the openings of the instrument are antinodes of the acoustic wave (as depicted below). What is the ...
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0answers
94 views

Boundary conditions for standing EM-waves

My freshman course on waves uses Young and Freedman's University Physics. They seem to argue in the following fashion: An electric field induced by a static charge distribution is conservative. When ...
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0answers
474 views

Boundary conditions for Navier-Stokes equations

The Navier-Stokes equations in combination with the continuity equation for incompressible Newtonian fluids is stated as $$\dfrac{\partial \mathbf{u}}{\partial t}+\left(\mathbf{u}\cdot \nabla\right)\...
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0answers
54 views

Connection between black body radiaton and cavitys

I have some questions concerning the relation between the black body radiation and cavitys. First of all, i don't see, why you can derive the black body spectrum from the mode density of the ...
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3answers
193 views

Conservation of Noether current

In Peskin equation 2.12 $$ \partial_\mu j^\mu(x) = 0, \quad {\rm for} \quad j^\mu(x) = \frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}\Delta\phi - \mathcal{J}^\mu $$ Why the current $j^\mu(x)$...
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1answer
417 views

Phase shift in reflection

Does every day-to-day life reflection cause a phase shift of pi? Or does this occur only in thin-film interferences?
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1answer
1k views

Periodic vs Open boundary conditions

In condensed matter, people often use periodic boundary conditions to perform calculations about bulk properties of a material. It's generally argued that in the $N\rightarrow\infty$ limit the ...
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1answer
102 views

Understanding boundary condition in this exercise

I am trying to do this quantum mechanics exercise: A particle with mass $m$ in the potential: $$V(x)= \left\{\begin{array}{lc}\infty& x\leq -a\\ \Omega\, \delta(x) & x>-a\end{array}\...
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1answer
129 views

Sound wave equation in 3D closed Box

We have the sound wave equation $\Delta p - \frac{1}{v^2} \frac{d^2}{dt^2} p = 0$ in a closed Box. So we got Dirichlet boundary conditions and I can combine the solution for the 1D case to a 3D ...
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2answers
989 views

Why my 4-divergence term added to a Lagrangian modifies the equation of motion?

I take this Lagrangian: $$\mathcal{L}=\mathcal{L}_0+\partial_\alpha f(\phi, \partial_\mu \phi).$$ In this topic Does a four-divergence extra term in a Lagrangian density matter to the field ...
2
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1answer
151 views

Boundary conditions in variational principles

In classical mechanics, the condition to fix the variation of the trajectory at the endpoints has a clear-cut meaning. We want the system to propagate from $x\in\mathcal{C}$ to $y\in\mathcal{C}$, ...
2
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1answer
330 views

Electric field due to infinitely charged plane does not satisfy boundary conditions

The field at the surface of a conductor is always $\frac{\sigma}{\epsilon_0}$. An infinite conducting plane has two faces, each with a surface charge density $\sigma$. The field at the surface is $\...
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0answers
86 views

Boundary condition on parallel component of B field

I am confused about the physical significance of discontinuity in the parallel component of B field. So the setup is let's say I have a cylinder with "frozen-in" magnetization M and a linear current ...
0
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1answer
647 views

Dielectric cylinder in uniform electric field: nonlong cylinder

Problem of dielectric cylinder in uniform electric field is well known. For example, Jackson textbook or Griffiths textbook or online solution here. Solution always given for case of long cylinder. ...
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1answer
277 views

Can someone intuitively explain image charges to me?

Ok, so here's what I understand from reading Purcell. There's the uniqueness theorem. This theorem says that given some assortment of conductors with fixed potentials at their surfaces (boundary ...
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0answers
134 views

Neumann boundary condition for Laplace's equation in 2D axisymmetric coordinates?

I have the Laplace's equation, say, describing the density $\rho(r,z)$ distribution in a 2D axisymmetric coordinate: $$\nabla^2 \rho=\frac{1}{r}\frac{\partial}{\partial r}\left(r\frac{\partial \rho}{\...
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2answers
486 views

Particle in 1D box. Different solutions for wavefunction

For a particle in a box $x$ ranging from $0$ to $L$ you get a solution of $\sqrt{2/L}\sin (n \pi x/L)$. But if you have a particle in a box $x$ ranging from $-L/2$ to $L/2$ infinite square well ...
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0answers
79 views

Numerical solutions with insufficient boundary conditions

Numerically is there a procedure to find at least one solution to differential equations given insufficient boundary conditions? For example: Consider electrodynamics in vacuum, and for initial ...
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2answers
82 views

Randomly initializing ensemble of particles in “toy” computer model

I'm programming a "toy" model, and want to intialize the $(\mbox{positions},\mbox{momenta})$ of an ensemble of particles in three-space, using a uniform (pseudo) random number generator. But I'm a ...
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0answers
279 views

Path integral defines a vector in Hilbert space

It is often stated that the path integral defines a state in the Hilbert space of the theory. I've seen this in low dimensional examples, with specific boundary conditions (for example paragraph 9.2 ...
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0answers
447 views

Why perpendicular component of Electric field is discontinuous across the boundary and parallel components continuous?

I was going through Griffith's electrodynamics boundary conditions and have a problem understanding the discontinuity of $E_\perp$ components. While deriving the electric field for an infinite sheet ...
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1answer
58 views

How can we justify $\psi(\textbf{r})\to\psi_{in}(\textbf{r})+\psi_{sc}(\textbf{r})$ at $|\textbf{r}|\to \infty$ but not at finite $|\textbf{r}|$?

In quantum scattering theory, the outgoing wave at $|\textbf{r}|\to\infty$, scattered from a localized potential, can be written as $$\psi(\textbf{r})\to\psi_{in}(\textbf{r})+\psi_{sc}(\textbf{r})$$ ...
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2answers
946 views

2D Schrodinger equation in polar coordinates - boundary conditions at the origin

When solving the Schrodinger equation in 2D polar coordinates, one has to deal with various Bessel functions. In the most simple example, the infinite circular potential well, the solutions to the ...
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1answer
170 views

Confusion about a boundary condition

In Griffiths' Electrodynamics book, there is an example in Chapter 4 (no. 7 in 4th edition). I am confused about the third boundary condition as shown in the image. How do we get that?