Questions tagged [boundary-conditions]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1
vote
0answers
44 views

Why we must impose this condition on the classical solution to employ the AdS/CFT dictionary?

I'm studying AdS/CFT and I have a confusion regarding conditions imposed on solutions to the KG equation in the bulk AdS. More specifically I'm considering the paper "Correlation functions in the ...
0
votes
2answers
65 views

Why wave function does not vanish at a Dirac delta potential?

I have studied that a wave function should vanish at the location of an infinite potential. Consider a direct Delta delta potential at $x=0$. Why does does function not become zero here at $x=0$?
1
vote
0answers
40 views

Boundary term for Chern-Simons action

As discussed in David Tong's lecture series on the edge modes in the quantum Hall effect (http://www.damtp.cam.ac.uk/user/tong/qhe.html) (page 203), varying the 2+1D Chern-Simons action yields: $$\...
0
votes
0answers
13 views

Solution for Inviscid Flow in a Moving Corner

I am considering the below situation (taken from page 26 of Fluid Mechanics by Landau and Lifshitz) where an inviscid fluid flows into a corner and is then turned back around. The corner is the ...
2
votes
3answers
151 views

Mathematics behind particle on a ring in QM [duplicate]

In QM particle on a ring, the Schrodinger in cylindrical coordinates is given by $$\frac{d^2\psi}{d\phi^2}=\frac{-2IE}{\hbar^2}\psi$$ where $I$ is the moment of inertia. Setting $ k^2=2IE/\hbar^2$, ...
1
vote
1answer
65 views

Green's function for free scalar field theory as an inverse of $-(\partial^2+m^2)$

In his book [QFT in a Nutshell], Zee argues that the functional integral $$Z= \int D\varphi \; e^{i\int d^4x[ -\frac{1}{2}\varphi(\partial^2+m^2)\varphi + J\varphi]}$$ can be evaluated by discretizing ...
2
votes
1answer
107 views

For energy eigenstates $\psi(x)$, does $\psi(x)\to0$ as $|x|\to\infty$ imply $E<V(\pm\infty)$ and vice-versa? If so, how can it be proved?

Let $\psi(x)$ be a solution of the time-independent Schrodinger equation (TISE) in one-dimension $$\psi''(x)+\gamma\left[E-V(x)\right]\psi(x)=0$$ where $\psi(x)$ is called an energy eigenfunction, $\...
1
vote
1answer
40 views

Where did the boundary conditions go in the frequency-space solution to the Green's function for a damped harmonic oscillator?

In differential equations, Green's functions are only defined given boundary conditions. In fact, you need two of them for a second order differential equation. In a lot of physics lecture notes, a ...
0
votes
0answers
16 views

Boundary condition (periodic) of many body wave function?

As we know, in a lattice system, the boundary condition for one body wave function is $\psi(N+1)=\psi(1)$. However, what is the exact periodic boundary condition for many-body wave function? To ...
1
vote
2answers
112 views

Laplace's Equation and Boundary Condition Problem

Calculate the potential and the electric field at point $P(r,θ,\phi)$, where $|r|> l/2$, due to a thin nonconducting rod of length $l$ that carries a total charge $Q$ that its uniformly distributed ...
2
votes
1answer
34 views

Coordinate transformation of boundary condition

Let us suppose a heat transfer problem inside a cylinder of radius $r_a$. If we neglect changes along $z$ and $\theta$ directions, i.e. only a cross section of the cylinder, the problem can be ...
0
votes
2answers
52 views

Wave function for particle in an infinite well located at $a$ and $b$ [closed]

I know that the wave function for a particle in a infinite potential well located between $0$ and $L$ is: $$\psi_n = \sqrt{\frac{2}{L}}\sin\frac{n\pi x}{L}$$ But I don't have idea how to apply ...
1
vote
1answer
19 views

Reflection and Transmission of String Waves

I was recently studying Waves and I came across a derivation of Amplitudes of reflected and transmitted waves in a string. Why have they used the highlighted conditions for the derivation?
1
vote
1answer
13 views

Is there a phase shift $\pi$ radians when a pressure wave is reflected upon a medium having less acoustic impedance?

In my text book it is written that a sound wave modeled as pressure fluctuations does not undergo a phase shift of $\pi$ radians upon reflection as there will be a pressure antinode at the interface ...
1
vote
0answers
29 views

Laplace Equation in Three Dimensions - Ball of Radius B

Consider the region $ V = {x ∈ R^3 | | x ≥ b }$ outside a ball of radius $b$ and a charge distribution $ρ$ in $V$ given by a point charge $q$ located at $y ∈ V$. Using the method of mirror charge, ...
0
votes
1answer
44 views

Counting $k$-states with periodic or fixed boundary conditions

When counting $\vec k$-states in a system - in my case, counting the number of states in the first Brillouin Zone - we either use periodic boundary conditions, $$\psi(\vec r) = \psi(\vec r + \vec L)$$ ...
2
votes
1answer
70 views

A-brane boundary conditions

This question concerns the boundary conditions that A-branes solve. Consider the following problem: Suppose that an A-brane wraps a submanifold $Y$ of $X$. Let $\mathcal{L} \rightarrow Y$ be a rank ...
0
votes
1answer
37 views

Regions separated by infinite potential

In normal (i.e. finite potential) QM systems, a particle wave function can have many nodes with $| \psi \rangle \neq | 0 \rangle \land \langle x | \psi \rangle = \psi(x) = 0$. However, in systems that ...
0
votes
0answers
32 views

Boundary conditions for radial solution of gauged topological vortices

I am following the book Topological Solitons by Manton and Sutcliffe and I am struggling to understand a boundary condition they choose to find the radial solutions of gauged vortices with finite ...
1
vote
2answers
51 views

Why do we generally get reflected and transmitted waves that too having same frequency as the incident one?

In a MIT OCW video lecture, a professor discusses a wave on a string having some density moving towards another string. Both of which are joined but have different densities. He goes on to analyse it,...
1
vote
1answer
43 views

What are the physical implications of these BCs to the 1D heat equation?

The heat equation in 1 dimension states that: $$\frac{\partial T(x,t)}{\partial t} = \alpha \frac{\partial^2 T(x,t)}{\partial x^2}\, , \quad \alpha > 0$$ And my boundaries on a finite rod of length ...
0
votes
1answer
49 views

Dirichlet boundary condtions in Nambu-Goto string action

The Nambu-Goto action for an open string with parameter domain $[0,\tau_1]\times[0,\sigma_1]$ is given by \begin{equation} S_{NG} = \int_{0}^{\tau_1} d\tau \int_{0}^{\sigma_1} \ d\sigma \ \mathcal{L}(\...
0
votes
1answer
72 views

Why is the solution of the radial Schrödinger equation valid at $r=0$?

The Schrödinger equation for a particle in a central potential is $$\left[\frac{p_r^2}{2m}+\frac{\ell(\ell+1)}{2mr^2}+V(r)\right]\psi(r,\theta,\varphi)=E\psi(r,\theta,\varphi).$$ This gives solutions ...
2
votes
1answer
62 views

What are the boundary conditions for an ideal fluid in a frictionless pool?

Suppose you want to numerically solve the classical 2D waves equation for an ideal incompressible fluid in a square pool. The pool's walls are frictionless, so the fluid could vertically move freely ...
2
votes
1answer
52 views

Brown-Henneaux Boundary Conditions

I am trying to reproduce the Brown-Henneaux boundary conditions stated in this paper (http://srv2.fis.puc.cl/~mbanados/Cursos/TopicosRelatividadAvanzada/BrownHenneaux.pdf). The paper constructs a set ...
0
votes
0answers
18 views

Continuity Conditions at a General Wave Boundary:

is there some general approach to deducing the continuity conditions at a wave boundary for any type of wave - quantum, string, pressure etc. that works for you in your physics. I find it difficult to ...
1
vote
1answer
29 views

Cases for reasoning about mass transfer

I'm doing some simulations of a 1D system with diffusion. One boundary has a no-flux boundary condition, while the other boundary has a prescribed-flux boundary condition with a specified mass ...
2
votes
0answers
31 views

Is there any relativistic constraint on the rate of change of a scalar field?

Consider a scalar field $\phi(t, x, y, z)$ obeying the waves equation with an Higgs-like potential (the "mexican hat"): $$\tag{1} \mathcal{V}(\phi) = \frac{\lambda}{4} (\phi^2 - \phi_0^2)^2, ...
1
vote
0answers
40 views

Quantum particle in the real projective plane $\mathbb{RP}^2$

Consider particles living in a $2D$ space with boundary conditions such that the space takes up a finite area. During introductory quantum mechanics classes, we are exposed to many examples, which I ...
1
vote
1answer
31 views

Wave function boundary condition in scattering problem

The the boundary condition for a wave function in a scattering problem is $$\psi_{\boldsymbol{k}_{1}}(\boldsymbol{r}) \underset{r \rightarrow \infty}{\rightarrow} A\left(\exp \left(\mathrm{i} k_{\...
-1
votes
1answer
55 views

Showing that with Dirichlet boundary values, the operator $\frac{\partial^4}{\partial x^4}$ is Hermitian [closed]

That is, that $\langle f, \frac{\partial^4g}{\partial x^4}\rangle = \langle \frac{\partial^4f}{\partial x^4},g \rangle$. I've been trying working by definition (for the first step), and using ...
1
vote
1answer
22 views

Why the exponential part of Electromagnetic waves on both side of interface must be equal?

Why the exponential part of Electromagnetic waves on both side of interface must be equal which implies equality of phases at the boundary at all the time to satisfy the boundary conditions. My text ...
0
votes
1answer
33 views

Why it is necessary that phase of incident, reflected and refracted wave must equal at the interface of two medium?

1.Why it is necessary that phase of incident, reflected and refracted wave must equal at the interface of two medium to satisfy the boundary conditions at the interface? 2. According to boundary ...
0
votes
0answers
20 views

Lane-Emden. Quasi-linearization method

ow to prove this theorem? I have a doubt. Theroem: Suppose that $w(x,\alpha)$ solved $\ddot{w}+\frac{2}{x}\dot{w}+\alpha^{2}w=0$ with $w(0)=1$, $\dot{w}(0)=0$, $w(1)=0$. Then $v(x,\alpha) := \omega w(...
0
votes
0answers
7 views

Set the boundary conditions for the electric field at the separation surface between a dielectric and an ideal conductor?

In an ideal conductor (sigma goes toward the infinite), there can be no electric field within it. But neither can there be a tangential component on its surface. Based on this, set the boundary ...
2
votes
1answer
32 views

Can the properties of a volume of space-time vacuum be determined by measurements just on its surface?

In classical electromagnetics, static electric and magnetic fields in a given volume in a vacuum are completely determined by measuring the fields on the surface that bounds the volume. The fields at ...
0
votes
0answers
9 views

BCs at 2D anisotropic media

I have 2D an-isotropic meta-surface with surface admittance $G = \begin{bmatrix} G_{xx}& G_{xy}&0\\ G_{yx}&G_{yy}& 0\\0&0&0& \end{bmatrix}$; the rest of the space is just ...
2
votes
2answers
94 views

Boundary conditions of a particle in a “topological” box

It is argued that the boundary conditions on a particle in a box (the box being a potential with value $0$ on the interval $[0,L]$ and infinite everywhere else) are $\psi(0) = \psi(L)=0$. Since the ...
0
votes
1answer
31 views

What is the physical significance of scale invariance (under appropriate boundary conditions) in the 1D Helmholtz equation?

So we were given this problem in mathematical physics (Context is that we're learning about Sturm-Liouville): Consider the 1D Helmholtz equation with $k^2>0$ $$\frac{\partial ^2y}{\partial x^2}+k^...
1
vote
1answer
34 views

Compactness condition on boundary formalism for loop quantum gravity

I'm going over Rovelli's Covariant Loop Quantum Gravity notes http://www.cpt.univ-mrs.fr/~rovelli/IntroductionLQG.pdf and in section 2.4.2 "Boundary formalism" he briefly develops how to ...
2
votes
2answers
110 views

Solving particle in a ring problem

While solving the particle in a ring we get a general solution of the form: $$\psi(x) = A\exp(imx) + B \exp(-imx)$$ Where $m=\left(\frac{2iE}{h}\right)^.5$. Imposing the boundary condition I get that $...
1
vote
0answers
30 views

Gauss's Law with Periodic Boundary Conditions- Why No Electrical Charges?

So I've read quite a few papers recently claiming that if you have a system with periodic boundary conditions, there are no electrical charges. I'm trying to better understand why this is the case. ...
0
votes
0answers
45 views

Is using periodic boundary conditions instead of fixed zero boundary conditions just for mathematical convenience?

In statistical physics, we get equivalent results for an ideal gas in a 3D box either if we fix the particle wavefunctions to be 0 on the box walls, or if we impose periodic boundary conditions so $\...
0
votes
1answer
68 views

Solution to heat equation with changing boundary conditions

I am attempting to solve a homogeneous heat equation \begin{equation} u_t = \alpha^2 u_{xx}, \end{equation} with an initial temperature $u_0$, and time-varying boundary conditions $u(0,t) = u(L,t) = ...
0
votes
1answer
40 views

Applying boundary conditions to discretized hamiltonian

I am trying to implement reflecting boundary conditions of $ \begin{align} \psi_N \equiv \psi_{N-1}, \end{align} $ $ \begin{align} \psi_{-1} \equiv \psi_0, \end{align} $ to the hamiltonian matrix and ...
1
vote
1answer
51 views

Equivalence Of Newton's Law and Leact action principle Without Math (Intuition): initial vs. boundary problem

First Let me write both the laws So Newton's law says that $$\mathbf{F}=m\mathbf{a}$$ and least action principle says that a particle occupy, at the instants $t_1$ and $t_2$, positions defined by two ...
1
vote
1answer
22 views

Confusion about boundary conditions for reflection of light

The reflection at a dielectric interface was analysed in Griffiths introduction to electrodynamics using the following diagram. I do not understand why the direction of $\vec E_r$ and $\vec B_r$ are ...
4
votes
1answer
70 views

Preparing States using path integral in QFT

I had some confusion about the idea of cutting the path integral to define states in quantum field theory. There are two versions which I have seen: We do the path integral with an unspecified '...
0
votes
1answer
52 views

How can we use the electrostatic boundary conditions for electromagnetic waves?

The boundary conditions for an electromagnetic wave passing from one linear dielectric media to the other (both having no free charges or current) are taken as: $$B_{\perp_1} -B_{\perp_2} =0$$ $${\...
1
vote
2answers
55 views

Boundary Conditions for a 3 point basketball 'swish' shot

(note: this is not a school project but a thing I'm trying to do in my free time) I am trying to model 3 point basketball 'swish' shot. A 'swish' is when a point is scored without the ball touching ...

1
2 3 4 5
16