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2
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28 views

Variation of Gibbons-Hawking-York term. General boundary condition and total derivatives

It is actually a comment and question to the answer of Robert McNees in the following post: Explicit Variation of Gibbons-Hawking-York Boundary Term In deriving the variation of the extrinsic ...
2
votes
1answer
116 views

How do you know when you need to use distributions to represent charge densities? [on hold]

I tried to solve a problem using Gauss' law in the following way. Let's assume we have a spherical shell of radius $R$ with a charge $Q$ being homogenously distributed on its surface. I am trying to ...
0
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1answer
31 views

Border conditions on the separation surface (Electromagnetism & Optics)

My teacher taught me that we can consider the following equation: $$E_{1t}=E_{2t}$$ to the descontinuity of the electric field tangent component on the separation surface of two means with ...
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0answers
74 views

A classically charged point particle interacting with electromagnetism and gravity

Consider a classically charged point particle interacting with electromagnetism and gravity. The relevant dynamical variables are $\chi^\mu (\tau)$ of the particle, the electromangetic potential ...
0
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1answer
38 views

Boundary condition for E field

My book says that the boundary condition for the E field is: $$\hat{n} \times (\textbf{E}_1 - \textbf{E}_2) = 0 $$ and then concludes that the above condition can be summarized by the statement, "The ...
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0answers
50 views

How to solve Laplace equation in a domain with one boundary along a curve?

Is there a way to solve the 2D Laplace equation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} =0$ on $0 <x<\infty$ and $0 < y < \infty$, such that the domain is ...
2
votes
2answers
99 views

Detailed conditions for symmetries of Lagrangian

Edit: To clarify the question, I am asking why we are justified in calling a continuous symmetry a symmetry of a system when it changes the Lagrangian by a total derivative of a function of $t, q(t)$ ...
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0answers
26 views

Magnetic dipole near black hole

Usually it is said that black holes cannot have electric or magnetic dipole, only electric charge and angular momentum are allowed quantities besides mass So, it would seem that black holes behave as ...
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0answers
27 views

Boundary conditions for vector wave equations

Assume the time-harmonic case of Maxwell's equations, one can obtain the following vector wave equations: $$ ...
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0answers
27 views

Why are closed strings with different perioidicities equivalent?

I was typing up some lecture notes the other day when I saw something unclear. While talking about bosonic open and closed strings and the Polyakov action, the notes say we don't need to distinguish ...
3
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2answers
137 views

Minimizing the Lagrangian action of an impossible problem

I'm working my way through Structure and Interpretation of Classical Mechanics (SICM), and am stuck on an exercise in Section 1.4: Exercise 1.6. Minimizing action: Suppose we try to obtain a ...
2
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0answers
49 views

Current Density Boundary Conditions and its Implications

According to Ohm's Law, one can say $ \overline{J} =\sigma \overline{E} $ if the field is in a conductor, and $ \overline{J} =0 $ if it's in empty space. Now if we take the surface of a conductor and ...
1
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1answer
45 views

Can Ampere's Circuital law be used on an infinite number of alternating Helmholtz coils?

I have the following surface current density $$ \bar{\sigma}_s = \hat{\phi} \sin(kz) |\bar{\sigma}_s| $$ to approximate an infinite number of alternating Helmholtz coils stacked along the z-axis with ...
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1answer
62 views

Boundary conditions of the radial Schrodinger equation

Consider the radial differential equation $$\bigg( - \frac{d^2}{dr^2} + \frac{(\ell+\frac{d-3}{2})(\ell+\frac{d-1}{2})}{r^2} + V(r) + m^2 \bigg) \phi_\ell (r) = \lambda\ \phi_\ell (r),$$ which I've ...
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0answers
18 views

What are maximally dissipative boundary conditions?

I ran into this term when reading about the initial boundary value problem in general relativity. They seem to be relevant when you need to impose boundary conditions on a timelike boundary, for ...
2
votes
2answers
213 views

Why do electric field lines start and end at 90 degree at the surface of a conductor? [duplicate]

There is one property of electric lines of forces which states that: Electric field lines start and end at 90 degree at the surface of the conductor. But why is that so? Is there any proof for ...
2
votes
1answer
167 views

Newton's law of cooling for the heat equation boundary condition

Newton's law of cooling says the temperature of an object satisfies $$ \frac{dT}{dt} = -k(T(t) - T_0),\tag{1} $$ where $T_0$ is the surrounding temperature. See these HTML notes for example. Now if ...
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0answers
60 views

Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain?

Let $\Omega$ be a domain in $\mathbb{R}^n$. Consider the time-independent free Schrodinger equation $\Delta \psi = E\psi$. Solutions subject to Dirichlet boundary conditions can be physically ...
4
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2answers
73 views

Why do we not require higher derivatives to match at boundary when solving the Schrödinger equation in a given potential?

When solving the time independent Schrödinger equation for a given potential in 1D, the main part of the solving involves matching boundary conditions. Usually, we require the value and the first ...
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1answer
33 views

How do i mathematically represent reflection in a (diffusion) Problem?

I am trying to formulate boundary conditions and it occurred to me that I never had to implement a reflective boundary before. The example is a one dimensional diffusion, where at $x=0$ the ...
0
votes
1answer
41 views

Fourier series for a wave on an infinite string?

From "Vibrations and Waves" by A.P. French I know that any wave on a string length $L$ can be represented by: $$y(x,t)=\Sigma^\infty_0 A_n \sin(\frac{n\pi x}{L})\cos(\omega_nt-\delta_n)$$ But can we ...
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2answers
66 views

When does $\mathbf n\times(\nabla V_2-\nabla V_1)=0$ imply $V_1=V_2$

I was reading a paper on electrohydrodynamics which has the following sentence (in my own words): At the interface/boundary, the requirement of continuity of the tangential component of the ...
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0answers
16 views

Phase change by reflection [duplicate]

Let's consider a light ray falling on a cuboid made of glass at the angle $\alpha$. Then there will be a reflected ray $A$. The ray will also refract. Let the refracted ray be $B$. Ray $B$ will be ...
2
votes
1answer
31 views

Could you give boundary conditions to the gravitational potential given the density distribution?

We´re doing a project that's all about solving differential equations with separation of variables. We´re trying to find the gravitational potential given the density distribution (that has azimuthal ...
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0answers
33 views

Electromagnetic boundary conditions for modelling symmetrical geometry

I stumbled upon this article: http://www.comsol.com/blogs/exploiting-symmetry-simplify-magnetic-field-modeling/ Since the article does not contain any mathematical formulations, I was wondering how ...
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0answers
25 views

How to specify boundary conditions as function of curvature in dynamic elastic beam pde?

In this article (already mentioned in this question) the dynamics of a planar elastic beam with "cantilever constrains" (one clamped end and one free end) is modeled. Using the Euler-Bernoulli Beam ...
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0answers
32 views

Neumann Green's function inside semi-infinite conductor [closed]

Consider a semi-infinite conductor with uniform conductivity $s$ occupying the space $z>0$. What is the Green's function with Dirichlet and Neumann boundary conditions inside the region $z>0$? ...
2
votes
1answer
39 views

How come a current sheet of $J_s = J_0 \hat{x}$ produces plane wave solution?

Given in the picture. There is a current sheet $J_s = J_0 \hat{x}$. Supposedly Jo is not oscillating. So, how does this thing create a plane waves propagating away from the current sheet? Shouldn't ...
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0answers
13 views

Solution for elastic wave on plane of ideal contact between two half spaces of elastic, homogeneous, isotropic, linear solids

Please give the solution for elastic wave of arbitrary polarization incident at arbitrary angle on plane of ideal contact (meaning no slip, homothermal, nondissipative, and no transfer of material ...
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0answers
12 views

Zero stress boundary conditions for the acoustic wave function

When is it appropriate to use zero normal stress boundary conditions when solving the acoustic wave equation. That is when the pressure is equal to zero.
3
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2answers
100 views

Idea behind Compactified Boson

On p. 167 of his Conformal Field Theory, Di Francesco introduces "Compactified Boson". He says: The invariance of the free-boson Lagrangian [...] with respect to translations $\varphi(x) ...
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0answers
35 views

Faraday's law in free space explaining away the constant vector?

Let's say that I have a plane electromagnetic wave travailing in free space, and I know the electric field part to be $\vec E$. If I am using Faraday's law to get the magnetic field part I will get ...
1
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1answer
146 views

Eigenvalues of the radial Schrödinger equation on a finite integration interval

There are numerous ways to estimate the eigenvalues of a radial Schrödinger equation, see http://arxiv.org/abs/math-ph/0703040 as an example. Anyhow, the formulas only cover the Schrödinger equations ...
2
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1answer
87 views

Question on boundary condition for Maxwell's Equations and Coulomb's law

When deriving Coulomb's law using the differential forms of Maxwell's equation, the boundary condition that $\phi = 0 $ at infinity is also used. From $\nabla × E = 0, E = \nabla \phi$ for some ...
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0answers
47 views

Terminal conditions and boundary terms in Lagrangian formulations: what do different choices mean?

For the sake of having compact expressions: $$ \left\langle f,g\right\rangle=\int^T_0 f(t)g(t)\,\text{d}t $$ Given some functional: $$ F=\frac{1}{2}m\!\left\langle ...
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1answer
79 views

Hamilton-Jacobi theory and initial value problem?

Having read through some recent posts regarding the Lagrangian formulation being interpreted into an initial value problem rather than the familiar boundary condition problem we are familiar with, I ...
0
votes
1answer
128 views

Meaning of boundary conditions in solid mechanics

The Question is: A uniform horizontal beam OA, of length $a$ and weight $w$ per unit length is clamped horizontally at O and freely supported at A. The transverse displacement $y$ of the beam is ...
0
votes
1answer
55 views

Losing a term for 3D radial schrodinger equation

I am trying to solve the Schrodinger equation For a potential $V(r)$ defined for $ 0<r<R$ as $$V(r)=-V_0 $$ and zero everywhere else. For wavefunction $u$ I can easily get to $$ u'' =-k^2u,$$ ...
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0answers
46 views

Deriving general boundary conditions from first principles for elastodynamic scattering

It seems that most of the relevant books only give the linear case and the rest say something along the lines of "here are common examples of boundary conditions." What are the most general boundary ...
0
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1answer
90 views

Lagrangian mechanics and initial conditions vs boundary conditions

It bothers me that many basic books on the classical mechanics don't discuss the following difference between "Newton's laws" and the "Principle of stationary action". Newton's laws can predict the ...
3
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0answers
86 views

Physical intuition for the solutions of the wave equation

I have been studying the wave equation in $\mathbb{R}^n$ for the cases $n=1,2$ and $3$. In the three cases, working all over $\mathbb{R}^n$. That is: $u_{tt}(x,t)=c^2 u(x,t)$ for $x \in ...
1
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1answer
93 views

Solving inhomogeneous differential equation with Green function

I'm not sure if this question is for physics forum, but my book's title is "Green's Functions in Quantum Physics", so I ask here. The book says that the Green's function defined as $$ (z-L( ...
8
votes
1answer
206 views

Why do we require quantum fields to vanish at infinity?

Classical fields, like the electrical field must vanish at infinity, because otherwise their energy would be infinite. This can be used in computations to exclude certain solutions. In quantum ...
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0answers
24 views

QM scattering in a finite-sized box

Background Consider a non-relativistic particle in a one-dimensional box of length $L$ with (for definiteness) an attractive delta function at the origin: $H = \frac{P^2}{2m} -|c|\delta(x), \qquad ...
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votes
0answers
64 views

General boundary condition for 1D heat equation

I'm studying from Numerical Solution of Partial Differential Equations by K.W.Morton and D.F.Mayers (Amazon link). I'm confused with general boundary conditions. Could someone give me a clue? For ...
0
votes
2answers
67 views

Phase change on reflection only 0 and $\pi$ allowed

We know that when a wave on a string is reflected from a hard boundary, the phase change is $\pi$, and from a soft boundary, the change is 0. My question is: this two conditions (hard and soft ...
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0answers
22 views

Lagrangian with a boundary contribution, external work and interaction

I am considering a linear second order partial differential equation of the form \begin{align} F(q,p)&=-a\,q-\nabla\cdot p=0\\ p(q,\nabla q)&=b\cdot\nabla q \end{align} with $a$ scalar and $b$ ...
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1answer
49 views

How does one show specific thickness and wavelength determine full transmission of electromagnetic waves?

How does one show that thickness and wavelength determine the full transmission between two different dielectric media if the boundary condition equations between two dielectric media are independent ...
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0answers
203 views

Is the principle of least action fully equivalent to the Euler-Lagrange equations?

I am citing from Landau and Lifschitz, this statement that will seem to you well-known, trivial, etc: "Between these positions, (i.e. $q_1$ and $q_2$) the system moves then in such a way that the ...
0
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1answer
33 views

Wave guide boundary conditions

Why only the normal component of Electric field and the parallel component of Magnetic field exist at the surface of a wave guide or any conductor?