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Questions tagged [boundary-conditions]

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433 views

Electric field boundary conditions proof

Good day I have a question regarding the boundary conditions proof: here is my question : in order to proof that the tangential component of the electric field are equal in the two mediums we start ...
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2answers
118 views

Physical meaning of this boundary value differential equation

(I originally posted this on math stack exchange but was advised to post it here) I am considering the following boundary value problem: $$-\frac{\mathrm{d}}{\mathrm{d}x} \left[ a(x) \frac{\mathrm{d}}...
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1answer
56 views

Charge on a conductor's surface

I take a charged conductor completely insulated. The charge is distributed over the surface, maintaining the surface at a given potential. The charge distribution that gives this potential is unique?
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1answer
174 views

What is intuition behind boundary condition on H field and magnetic field B?

I read about boundary conditions, perpendicular and parallel components below and above the surface in Griffiths' "Introduction to Electrodynamics" book. I'm unable to understand it intuitively. Can ...
-1
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1answer
446 views

A point charge near an infinite conducting plane

I want to calculate (with Poisson's equation) the electric field in the region containing a point charge near an infinite conducting plane with 0 potential. My textbook uses V(x,y,z)= 0 for every x,y,...
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1answer
69 views

Why is flux at an interface purely diffusion?

In many textbooks, the flux at the point of interface of two phases/regions is given through Fick's first law, with purely diffusive flux, even when there can be bulk convection in both phases/regions....
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2answers
582 views

How do I show that the Laplace equation has a unique solution under the Dirichlet closed-surface boundary condition?

In other words, when the the potential is specified at a finite boundary, how can I show the solution to $\nabla ^{2} V = 0$ exists and is unique? It is fine to show it for two dimensional Cartesian ...
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1answer
83 views

What is the importance for the pressure/velocity at infinity be constant in fluid dynamics?

I am studying fluid dynamics on my own and it is commom to see this assumption. I am asking this here because I didn't find any satisfactory answer. For example, I am studying a problem that is as ...
2
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1answer
339 views

Is this expression for radial probability flux in Sakurai's Modern Quantum Mechanics wrong?

The section on Schrodinger's equation for central potentials in Sakurai's Modern Quantum Mechanics (p. 208, 2nd edition) contains the following expression for the radial probability flux, as part of ...
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0answers
56 views

Trouble applying boundary conditions to Laplace equation

I'm having trouble finding which conditions to apply to Laplace equation in order to find the electrostatic potential of a specific configuration: There are 4 electrodes, given by the equations (each ...
0
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1answer
49 views

Viscous force between fluids

Why do we say that the viscous force between the flow of two different fluids is the same, in the boundary conditions? Shouldn't it be symmetric, once there must be an action reaction from the 3rd law?...
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2answers
81 views

Can we somehow extract the solutions for a free particle from the solutions to the infinite square well, in the limit that $a\to\infty$

The stationary state solutions to the infinite square well potential are given by, $$\psi_n(x)=\sqrt{\frac{2}{a}}\sin \left(\frac{n\pi x}{a}\right).$$ The energies corresponding to these states are $$...
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4answers
700 views

Why do the energies of the infinite square well decrease as width of the well increases?

The stationary state wavefunctions for the infinite square-well of width $a$ are given by $$\psi_n(x)=\sqrt{\frac{2}{a}}\sin{(\frac{n\pi x}{a})}.$$ These correspond to energies, $$E_n=\frac{n^2\pi^2\...
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2answers
294 views

Solving the TISE for Infinite square well mathematical question

Consider the infinite square well situation where the potential is infinite at positions $|x| > a$ and $0$ otherwise. When solving the Time independent Schrodinger Equation (TISE) we can come to ...
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1answer
438 views

1D Time independent Schrodinger equation applied to a ring of Radius $R$

In the lectures we have been doing basic examples of Applying the TISE to determine the solutions of simple situations such as the finite and infinite square well and I understand how to find the ...
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1answer
155 views

Energy spectrum for a step potential

Most of the books tend to give this explanation that for a bound physical system, the energy and momentum eigen values have discrete spectrum and otherwise, they have a continuous spectrum, which I ...
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1answer
689 views

Discontinuity of wave function derivative

In general, apart from mathematical standpoint, physically what causes the discontinuity of the derivative of wavefunction at infinitely high discontuinity of potential, but not in the case of a ...
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1answer
58 views

Significance of the order of derivatives in an action

What is the significance of having higher order derivatives in an action describing some system? For example, suppose I have the following two actions \begin{align} S_1&\propto \int \text{d}^4x \...
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1answer
137 views

Velocity field to a permeability field using poisson pressure equation

I have a velocity field and I want to get a pressure field. In my experiment we're controlling the pressure at the inlet and the outlet. I have Dirichlet boundary conditions at the inlet and outlet ...
2
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4answers
188 views

What is the physical meaning of the statement ''Lagrangian can only be defined up to a total derivative"?

Considering an analogue for potential energy of a physical system, it can be unique up to an additive constant but this can be explained on the ground that we are really interested in the change of ...
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0answers
87 views

Example of Analytic Solution to 2+1D Maxwell Equations with Dirichlet Boundary Conditions

Just curious, could someone point me to an analytic solution to 2+1D Maxwell equation on a rectangular domain with Dirichlet Boundary Conditions. With the pertinent information regarding the boundary ...
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2answers
303 views

Why does energy loss cause end corrections?

Several people have said that end corrections occur because of acoustic radiation or something similar, where energy is used in vibrating the air outside the pipe. How exactly does energy loss cause ...
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2answers
1k views

Intuitive Cause for End Corrections

I have looked for an intuitive description for the reasons for end corrections. I find most of them with mathematics far beyond my level (high school). I found two sites that attempted to explain it, ...
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1answer
1k views

How is the relationship between the end correction and the pipe diameter related to acoustic impedance?

I know that Levine and Schwinger calculated the exact value of the end correction by doing something with the acoustic impedance but I don't understand their calculations. I've looked at paisanco's ...
2
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2answers
93 views

Incorrect result for a standing wave on a rope with free ends [closed]

Given a rope with both ends free, the general solution is $$\psi(x,t)=f(x-vt)+g(x+vt),$$ such that $$\frac{\partial\psi}{\partial x}(0,t)=0=\frac{\partial\psi}{\partial x}(L,t).$$ Question If $f(x-...
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1answer
873 views

The boundary conditions in a waveguide

Suppose a cubic waveguide, made of perfect conductor, has only two open parallel sides. And the boundary conditions in this case are that the electric field at the surface must satisfy: $$\vec{B} \...
1
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1answer
148 views

Fluid-solid coupling, how to impose both normal stress and velocity?

I'm trying to solve the coupled Navier-Stokes/elasto-dynamics equations using a discontinuous Galerkin approach in order to propagate waves through a fluid-solid interface. I was wondering how to ...
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1answer
26 views

An electrostatic problem for two disks in $\mathbb{R}^2$ - how can the solution be represented?

The electrostatic Laplace problem for the exterior of a disk can be solved in a straightforward manner using separation of variables. Suppose we have a unit disk $\Omega$ with a charge density of $f$ ...
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1answer
498 views

What is the logic behind box normalization and periodic boundary condition?

Free particle energy eigenfunctions are $A\exp{[i(Et-\textbf{p}\cdot\textbf{r})/\hbar]}$ are non-normalizable. To normalize them one introduces a procedure called 'box normalization' where one imposes ...
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2answers
311 views

Why is magnetic field parallel to the surface of a conductor?

On Jackson- Classical Electrodynamics it is said that, for a perfect conductor the magnetic field is always parallel to the surface, that is $$\mathbf{B} \cdot \mathbf {n}=0$$ I do not understand ...
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1answer
605 views

Why the variation of a surface term is zero?

My original question is like: Why are the Euler-Lagrange equations invariant if we add a surface term to the action? And there is an answer by Javier: https://physics.stackexchange.com/a/...
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0answers
63 views

Why is Hamilton's Principle not the 'Principle of Least Action'? [duplicate]

Hamilton's Principle is that the first order variations of $\displaystyle\int^{t_2}_{t_1} L$ $ dt$ for an on-shell trajectory in the configuration space should vanish provided the varied off-shell ...
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0answers
63 views

How to solve equations with jump condition?

Consider two regions $\Omega_1, \Omega_2$ that are separated with a surface $\Sigma$. In Region $\Omega_i$ one has the wave equation $$\partial_t^2 u - c_i^2 \partial_x^2 u = 0,c_i = \sqrt{\frac{E_i}{...
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0answers
66 views

Boundary condition of graviton fluctuations

When computing Euclidean gravitational path integral, one expands around a saddle point, and naturally there is a classical part and a one-loop part (and more). In particular, the one-loop part can be ...
2
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1answer
988 views

Why does the Neumann boundary condition represent no flux?

I have heard that the Neumann boundary condition $$ \frac{\partial p}{\partial n} = 0, $$ for the acoustic pressure field in the Helmholtz equation in acoustic wave is related to flux. But we normally ...
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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
89 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
50 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
209 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
55 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
407 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
134 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
405 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
42 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
53 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
79 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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1answer
344 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
85 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
67 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 ...