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2
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1answer
26 views

String boundary conditions

I'm reading Polchinski and am confused about equation (1.3.13), $$\gamma_{\tau\sigma}\partial_\tau X^\mu-\gamma_{\tau\tau}\partial_\sigma X^\mu=0~~~~~\text{at}~~~~~\sigma=0,l.$$ It says that this ...
0
votes
0answers
57 views

Differential Equations [on hold]

$$ \nabla^2 B = - \mu_0^2 \epsilon_0^2 \frac{\partial B}{\partial t} $$ $$ \nabla^2 E = \mu_0 \epsilon_0 \frac{\partial B}{\partial t} $$ Find as many E and B field solutions as you can from this. ...
1
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0answers
28 views

Contradictory boundary conditions in electrostatics problem?

Consider the following problem: A conducting cube of side $a$ is grounded. Inside there's a horizontal (i.e., perependicular to the $z$ axis) sheet with uniform surface charge density $\sigma$. The ...
0
votes
2answers
33 views

No-slip boundary condition for viscous fluids

When dealing with fluid mechanics of viscous fluids, both theoretically and numerically, I've always been told that the boundary condition applied at solid walls has to be a no-slip one. My teachers ...
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0answers
49 views
3
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3answers
67 views

How does a photon “know” that it's left one charge and that it's going to another one?

How does it know the same charge it left will be the same charge it will return to? My understanding is photons are neutral and have no charge. i.e. Like charges repel, unlike attract. All charged ...
1
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1answer
44 views

Does charge distribute itself uniformly on a conductor?

An excerpt from a beginning E&M book [...] In other words, the surface of a conductor is an equipotential surface under static conditions. [...] Summarizing the boundary conditions at the ...
2
votes
1answer
48 views

Magnetic Field in the presence of a conductor

I am studying for my quals and came across an old question that reads like the following: There are two regions in space separated by an infinite conducting plane. Region 1 has a magnetic dipole ...
2
votes
1answer
41 views

Conserved charges given conserved current via Noether's theorem

Let $j^{\mu}_{a}$ be the conserved current associated with an infinitesimal symmetry transformation, cf. Noether's theorem. The conserved charge associated with $j^{\mu}_{a}$ is $$Q_a = \int d^{d-1}x ...
2
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0answers
36 views

Self-adjoint extensions with 'teletransporting' boundary conditions

When choosing a self-adjoint extension of a Hamiltonian, in general one can obtain domains in which (i) the probabilities teleport* between points on the boundary and (ii) boundary conditions ...
0
votes
1answer
82 views

How we know this solution is unique?

A typical problem where we exploit the uniqueness theorem towards a solution, is finding the potential outside two cylindrical parallel conducting wires (at potentials $V_0$ and $-V_0$) extending to ...
0
votes
1answer
62 views

Is there a surface charge density?

Consider a dielectric sphere placed within a dielctric medium. There is a uniform electric field $E_0$ present throughout in the medium. Would there be surface charge on the sphere?
2
votes
2answers
94 views

The nature of “hard wall” boundary condition for Schrodinger's equation

For a quantum particle in an one-dimensional infinite well of width $L$, the potential has the formal expression: $$ V(x) = \begin{cases} \infty, & x < 0 \\ 0, & 0 \le x \le L \\ \infty, ...
1
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2answers
35 views

Snells Law: Does the $k$ vector change on the boundary between mediums?

I was using Waves - Berkley Physics Volume III, and in explaining Snell's Law the author claims that as a wave is on the boundary between glass and air (going from glass to air) that the number of ...
2
votes
1answer
91 views

Laplace's Equation - under what circumstances does it hold?

I'm currently taking an EM course whereby we deal with systems that satisfy Laplace's equation $\nabla^2 \phi = 0$. Examples include permeable sphere in a magnetic field and metal sphere in electric ...
6
votes
1answer
97 views

Green function two solutions questions

I am having some trouble with Green functions in electrostatics What is the meaning of this trick: Given $$\vec{\nabla}^2 V(\vec{r}) = \frac{-1}{\varepsilon_0}\rho(\vec{r}) = ...
3
votes
1answer
117 views

Solving non-linear ODE for divalent solution at a 1-D surface boudary

I am trying to solve the following equation for a positively charged plane with charge density $\sigma$ at $z = 0$. $$ \phi''(z)=-\frac{e}{\epsilon \epsilon_0} \big(z_+n_{+} e^{-\beta z_+ ...
3
votes
0answers
192 views

Derivation of Euler-Lagrange equations for Lagrangian with dependence on second order derivatives

Suppose we have a Lagrangian that depends on second-order derivatives: $$L = L(q, \dot{q}, \ddot{q})$$ If we're working on the variational problem for this Lagrangian, then I know that we'll wind up ...
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0answers
42 views

How do I get around the fact that boundary conditions don't apply in the equation's region of validity?

A tight string lies along the positive x-axis when unperturbed. Its displacement from the x-axis is denoted by $y(x, t)$. It is attached to a boundary at $x = 0$. The condition at the boundary is ...
2
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0answers
41 views

Has this boundary condition been used in fluid flow?

I would like to know whether anyone has seen a boundary condition used in a fluid flow problem, of the following type. Suppose viscous incompressible fluid is to the left of a plane $x_1=a$, so the ...
1
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0answers
38 views

Wannier functions on a ring

Let's say I have a single particle hamiltonian in a periodic potential. For example a 1D lattice such that: $$H = -\frac{\partial_x^2}{2m} + V(x) $$ with $ V(x+a) = V(x)$ where $a$ is the lattice ...
0
votes
1answer
87 views

Finding the odd parity bound state wave function for a particle in one dimension

Let a particle of mass $m$ and energy $E$ be moving on the $x$-axis in a potential $V(x)$ given by $$V(x)=\left\{\begin{matrix} -V_{0}, & -a<x<a\\ 0, & otherwise \end{matrix}\right.$$ ...
-1
votes
1answer
86 views

Boundary conditions for the heat equation when solving a mass density gradient

I'm working with a mass density gradient with length $L$ and I'm trying to solve the heat equation in 1-D (mass diffusion equation, $\partial_t\rho(t,x)=D\Delta\rho(t,x)$), but I'm not sure which ...
1
vote
0answers
111 views

Sommerfeld radiation conditions for an electromagnetic field

There is some confusion in the definition of Sommerfeld radiation conditions for an electromagnetic field, which are related to the asymptotic behaviour of the field for a distance $r \to \infty$ ...
1
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0answers
113 views

Electromagnetism - Proof of the Uniqueness theorem for an external problem

In the electromagnetic Uniqueness theorem, we consider a volume $V$ enclosed by a surface $S$. It is initially assumed that two different fields are valid solutions for the Maxwell's equations with ...
6
votes
2answers
77 views

Why are holomorphic boundary CFT2 primary operators massless in the AdS3 bulk?

I saw a claim in this paper that holomorphic boundary CFT$_2$ primary operators correspond to massless states in the AdS$_3$ bulk. Specifically, As always, we simplify the situation by assuming ...
1
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0answers
34 views

Derivation of Boundary Conditions

Source: http://my.ece.ucsb.edu/York/Bobsclass/201C/Handouts/Chap1.pdf (page 6). I am trying to make sense of the derivation on the right side of these two integrals. The first one which says ...
3
votes
1answer
125 views

An Electric Potential Glued to a Cubic Insulator to Replicate a Point Charge: Charge Distribution

I have been going back over this problem with a friend for the better part of a day: A potential is glued to a cube insulator so that outside of the insulator the field is the same as a point ...
2
votes
1answer
56 views

Solving the 1-d time-independent Schroedinger's equation with an infinite boundary

In my introductory modern physics class we have examined time-independent solutions to the Schrödinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles ...
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0answers
49 views

Derivation of cylindrical line heat source problem?

I have a line heat source embedded inside a cylinder and I am trying to find the temperature distribution T(r,t). By using the similarity variable, the solution to the differential equation is ...
1
vote
1answer
47 views

Can I apply symmetry to this boundary value problem (BVP)?

Let's say I have a hollow cylindrical shell with inner radius $a$ and outer radius $b$ and length $L$. The temperature at at z=L is $T_{2}$ and the temperature at z=0 is $T_{1}$. There is also an ...
1
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0answers
66 views

Equivocal boundary conditions for Laplace equation of 2D “V”-shape conductor

A two dimensional infinite "V"-shape wedge conductor is earthed, wherein $\beta$ is the intersection angle. We can solve Laplace equation so as to get the electric potential inside the "V" zone, as is ...
1
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1answer
97 views

Normal to the Hypersurfaces

I am trying to understand the derivation of the Hilbert-Einstein action. However it requires a knowledge about hyper-surfaces for the boundaries of the integrals and also about the normal to the ...
3
votes
1answer
102 views

Is the system of equations of electrostatics underdetermined or overdetermined? [duplicate]

The following equations are equations of electrostatics: $$\nabla \times \vec E=0$$ $$\nabla\cdot\vec E=\dfrac{\rho}{\epsilon_0}.$$ These are 4 independent equations, while $\vec E$ has only 3 ...
4
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3answers
410 views

Comparison of 1D and 3D wave functions

When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy ...
0
votes
1answer
108 views

Axisymmetric fluid flow

I'm having trouble with a boundary condition. In a fluid mechanics problem, I have flow at $z = \infty$ flowing into a solid plate at $z = 0$ and then flowing radially, and the problem is given as ...
2
votes
3answers
291 views

Does a four-divergence extra term in a Lagrangian density matter to the field equations?

Greiner in his book "Field Quantization" page 173, eq.(7.11) did this calculation: ${\mathcal L}^\prime=-\frac{1}{2}\partial_\mu A_\nu\partial^\mu A^\nu+\frac{1}{2}\partial_\mu A_\nu\partial^\nu ...
0
votes
1answer
434 views

Interpretation Born-Von Karman boundary conditions

The cyclic Born-Von Karman boundary condition says that if we consider a one dimensional lattice with length $L$, and if $\psi(x,t)$ is the wavefunction of an electron in this lattice, then we can say ...
2
votes
1answer
137 views

How many kinds of topological degeneracy are there?

Here I want to summarize the various kinds of topological ground-state degeneracy in condensed matter physics and want to know whether there exists any other kind of topological degeneracy. For ...
0
votes
1answer
648 views

Boundary condition for a floating electrostatic potential

I have a (probably) simple question regarding boundary conditions. In electrostatic simulations, the relevant Maxwell equation is $\nabla \cdot \mathbf{D}=\rho$ where $\mathbf{E}=-\nabla V$, and ...
4
votes
1answer
150 views

Boundary conditions on current carrying wire

I'm trying to simulate by finite elements method Maxwell equations for a current carrying wire. My 3d geometry consists of a cylinder and a box containing it. I will use a mixed formulation and ...
12
votes
1answer
426 views

Asymptotic symmetry algebra

So after a lot of research, and tons and tons of papers that I've went through, I finally have some idea how to solve the equations that will give me candidates for the asymptotic symmetry group for ...
3
votes
5answers
728 views

Infinite Wells and Delta Functions

In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of ...
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votes
2answers
535 views

Meaning of boundary condition for steady current density?

Although I understand the derivation of boundary condition in case of steady electric current but I did not understand, that the electric field which is in direction of $J$ current density that is ...
2
votes
1answer
70 views

Getting diffeomorphisms from boundary conditions in $AdS_3$

As usual I'm asking a question about boundary conditions for AdS${}_3$, based on the thesis by Porfyriadis. He is solving equations $\mathcal{L}_\xi g_{\mu\nu}$ for AdS${}_3$ metric, with a given ...
2
votes
2answers
263 views

What restrictions on time boundary conditions does it have to use Fourier transform to solve wave equation?

The wave equation can be solved using Fourier transform, by assuming a solution of the form of $$\mathbf{E}(x,y,z,t)~=~\mathbf{E}(x,y,z)e^{j\omega t}$$ and then reducing the equation to the Helmholtz ...
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2answers
164 views

Complex Versus Real Wave Velocities in Quantum Mechanics

There's a fantastic quote in Schrodinger's second 1926 paper1 that apparently provides some motivation for the discrete energy levels (I think) that I'm having trouble interpreting: I would not ...
2
votes
1answer
64 views

Finding superpotentials and central charges in $AdS_3$

In text "Covariant theory of asymptotic symmetries, conservation laws and central charges" is given an example of finding central charges and superpotential (among other things). I am interested in ...
2
votes
1answer
451 views

How to solve bound states of 2D finite rectangular square well?

I want to solve bound states (in fact only base state is needed) of time-independent Schrodinger equation with a 2D finite rectangular square well \begin{equation}V(x,y)=\cases{0,&$ |x|\le a ...
1
vote
1answer
121 views

A question about Poincare invariance of Polyakov action

I have a question the variation of the Polyakov action, related to this Phys.SE post. For Polyakov action $$ S_p[X,\gamma]=-\frac{1}{4 \pi \alpha'} \int_{-\infty}^{\infty} d \tau \int_0^l d \sigma ...