Questions tagged [boundary-conditions]

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70 views

Incompressible 2D Navier-Stokes equation

I am trying to solve for and simulate the vorticity numerically (finite difference method), however there's one part I was hoping to get some help with. I need to find the fluid velocity $\mathbf{u}$ ...
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2answers
426 views

What does asymptotically flat solution mean?

Can somebody explain what does it mean when a solution is "asymptotically flat"? like the schwarzschild metric which is asymptotically flat solution to vacuum Einstein equations.
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0answers
48 views

How do waves get reflected at open end of an organ pipe? [duplicate]

Inside and outside of an open organ pipe usually medium used to be same (if i am not wrong) i.e Air, so in order to get standing wave reflection of wave is needed ( opp.in direction nd of same ...
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1answer
3k views

Understanding free slip boundary condition

In fluid dynamics, free slip boundary condition is equivalent to absence of tangential shear stress along the boundary. But then, in what sense is the word "free" used here? Does it mean that the ...
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2answers
827 views

Why are wave functions required to vanish at infinity?

I'm taking an introductory quantum mechanics class and although we require the wave function to (rapidly?) decay at infinity, I'm not entirely sure why. I have no background in physics (I took AP ...
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1answer
135 views

How is Neumann's green function found for a particular surface?

Green's Functions can be used to solve boundary value problems. In particular, there is a textbook standard recipe for dealing with von Neumann boundary conditions. But how can I find a particular ...
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3answers
197 views

Why do we need a second equation for electric field in Maxwell's Equation?

Suppose we are dealing with electrostatics for this question. A physicist carries out experiments with static charges and determines that, the electric field $\vec { E } (\vec { r } )$ is a quantity ...
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1answer
27 views

EM Radiation with Oblique Insidence of Dielectric Boundary

So in my university course, we have studied the EM radiation infalling perpendicularly onto a dielectric boundary. I have now tried to go beyond and work out how the relationships look for oblique ...
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1answer
67 views

Confusion regarding light [duplicate]

I have two question about light: When a light wave travels from free space to a medium then there is a change in the amplitude. Why? when a wave changes its medium then its frequency does not change ...
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2answers
125 views

Behavior of potential by infinite charge distribution

The picture is a question from the book Intro to Electrodynamics by Griffiths. In question as you can see we want to find potential due to an infinite strip maintained at constant potential in the ...
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2answers
632 views

Why does Griffiths's book say that there can be no surface current since this would require an infinite electric field for an incident wave?

In sec. 9.4.2 Griffiths shows the well known boundary conditions for E and B fields, one of them is this: $$\frac{1}{\mu_{1}}\textbf{B}_{1}^{\parallel}-\frac{1}{\mu_{2}}\textbf{B}_{2}^{\parallel}=\...
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1answer
94 views

Half-line vs radial Schrodinger equation

Assume that a quantum particle is constrained to move along a semi-infinite fixed rigid rod. This system could be described as a particle on a half-line, if we introduce the cartesian coordinates so ...
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3answers
106 views

Proving that the 3-current density corresponding to the global phase invariance vanishes at infinity

The components $j^i$ of the 3-current density $\textbf{j}$ corresponding to the global phase invariance of the action of a complex scalar field $\phi$ i.e., $\phi\to e^{-iq\theta}\phi$ is given by $$...
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1answer
564 views

Linear, homogenous and isotropic dielectric in electrostatic field. Why do I consider two potentials (inside & outside sphere)?

Presentation of the problem : We have a uniform homogenous isotropic dielectric sphere in an electrostatic field. To solve this problem, we remark that we have an azimuthal symmetry. So the ...
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1answer
150 views

Understanding electric field discontinuity

From divergence theorem/Gauss's law: $$\oint_S \vec{E} . d\vec{a}=\frac{1}{\epsilon_0}\sigma A.$$ From what I understand, Gauss's law is where the electric field discontinuity (at a boundary) is ...
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3answers
482 views

$\sin$ and $\cos$ components in symmetric infinite potential well problem

Consider an infinite potential well in one dimension with boundaries at $\pm a/2$. Can $\psi(x) = A \sin(kx) + B \cos(kx)$ for this system? The way it was answered was "mathematically acceptable but ...
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2answers
148 views

What subset of the Hilbert space is a physical state?

Not all Hilbert space vectors are generally considered physical, due to various reasons. A particular example (as found in Hall's "Quantum mechanics for mathematicians") is the classic particle in a ...
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1answer
82 views

What is the essential difference between the orbifold $S_1/Z_2$ and an interval say, $[0,1]$?

As the title asked, what is the essential difference between the orbifold $S_1/Z_2$ and an interval say, $[0,1]$? I mean $S_1$ can be [-1,1] with -1 and +1 identified. Now $S_1/Z_2$ then is just [0,1]...
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1answer
150 views

Free charges and boundary conditions [closed]

I'm having some trouble with the following problem: Consider a plate of a dielectric material homogeneous and isotropic with a dielectric constant equal to er= 2 , in the outside we have a uniform ...
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1answer
361 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
108 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
55 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
149 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 ...
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1answer
382 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
57 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
434 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
73 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 ...
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1answer
307 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
50 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 ...
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1answer
45 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
80 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
511 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
247 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
391 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
145 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
535 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
53 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
130 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 ...
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4answers
180 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
79 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
289 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
879 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
893 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 ...
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2answers
89 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
703 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} \...
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1answer
132 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
456 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
274 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
509 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/...