We’re rewarding the question askers & reputations are being recalculated! Read more.

Questions tagged [boundary-conditions]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
2
votes
1answer
156 views

Boundary conditions for Quantum Cascade Laser (QCL)

The Quantum Cascade Laser (QCL) is a semiconductor device for the generation of radiation in the MIR region of the electromagnetic spectrum. One period of the device consists of two regions, the ...
2
votes
2answers
211 views

What is the interpretation of a wave function of the Universe in Hawking's no boundary proposal?

In the path integral formalism we have an in state $\Psi_{in}[\phi]$ and and out state and we find the amplitude for going from one to the other: $$\Delta[\Psi_{in},\Psi_{out}] = \int \Psi_{in}[\phi]...
1
vote
2answers
84 views

Heat Equation… with Newton Cooling?

I have the following differential equation that is purported to represent the equilibrium temperature at a point $x\in [0,L]$ on an uninsulated rod of length $L$, whose end points are kept constant $T(...
0
votes
3answers
799 views

Particle in a box, quantization of energy

I'm learning about how the energy of matter is quantized like how the energy of light is. My textbook illustrates the concept of quantization with the particle in a box: "A particle of mass $m$ ...
1
vote
2answers
38 views

Are the boundary conditions purely a consequence of Maxwell's equations?

The boundary conditions, namely were all these, realized only by looking at Maxwell's equations? Or is there a physical reasoning behind them? For example, Why does the component of the electric ...
0
votes
1answer
37 views

Jackson Green function expansion in spherical coordinates

In Jackson's "Classical Electrodynamics" third edition in section 3.9 page 121 while explaining a Green function expansion the following equation is attained: $ \frac{1}{r}\frac{d^2}{dr^2}(rg_l(r,r'))...
0
votes
2answers
207 views

Boundary condition for Schrödinger equation at metal-semiconductor interace

Suppose I want to solve the 1D, time-independent Schrödinger-equation for a metal-semiconductor junction. In the metal region $0 \leq x \leq x_{0} $ the Schrödinger equation reads: $(-\frac{\hbar^2}{...
2
votes
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 ...
0
votes
1answer
244 views

Understanding boundary conditions in heat transfer

In the context of heat transfer, how does one physically interpret the following boundary conditions: $$ u \cdot \mathbf{n} = 0, \qquad \frac{\partial u}{\partial \mathbf{n}} \cdot \tau = 0 $$ where $...
2
votes
1answer
168 views

Fixing time in Feynman phase space path integral

The phase space version of Feynman's path integral expression for the free particle propagator involves a (formal) sum over paths in phase space with fixed $q$ endpoints and (as far as I'm aware) ...
1
vote
0answers
15 views

Delta Potential Boundary Conditions on the wavefunction

I'm reading over how the delta function potential problems are solved and I can't really understand the origin of these boundary conditions: $(1) \,\,\psi \,\,$ is always continuous $(2) \,\, \dfrac{...
3
votes
1answer
549 views

Why must this boundary condition be met? (Electromagnetic wave at interface between two mediums)

My textbook says that The laws of Electromagnetic Theory (Section 3.1) lead to certain requirements that must be met by the fields, and they are referred to as the boundary conditions. ...
0
votes
0answers
41 views

No boundary conditions approach in cosmology

I have the following questions about James Hartle and Stephen Hawking's 'No-boundary' proposal: In their approach multiple histories would exist. These histories could yield universes with different ...
2
votes
2answers
91 views

Free particle on a Möbius strip: boundary condition

I've just see this video ( https://youtu.be/np6_1k99oRA ) and this guy tried to calculate the eigenvalues of a free particles on a Möbius strip using the boundary condition on the rectangle $[-\infty,\...
2
votes
1answer
292 views

Why is the total force at a free surface zero?

I am looking into waves on a free surface for which their are two main conditions: Kinematic condition: Particles on the surface remain on the surface. Dynamic condition: Forces acting on the surface ...
9
votes
1answer
192 views

What are the energy eigenstates for a modified quantum harmonic oscillator?

Imagine a particle obeying Schrodinger's Equation with an harmonic oscillator potential modified with an additional linear potential and cut off with an infinite potential barrier at $x=0$. That is, $$...
3
votes
1answer
117 views

Quantization of Klein-Gordon field between two boundaries

Consider a real scalar $\phi(x,t)$ with mass $m$ in $1+1$ dimensional spacetime, described by the 2d free Klein-Gordon action. $\phi(x,t)$ lives on an interval $0 \leq x \leq L$, and is subject to ...
1
vote
1answer
42 views

Potential of hydrogen atom solution of the Laplacian: Missing boundary condition to fix integration constant $c_1$

I have following problem, I want to calculate the classical potential $\phi(r)$ of the hydrogen atom in its ground state. The charge density is known: $$\rho(r)=\frac{-e_{0}}{\pi a^3}e^{-\frac{...
3
votes
1answer
98 views

Understanding Periodic and Anti-periodic boundary condition for Jordan-Wigner transformation

In the study of spin chains with periodic boundary condition ($S_{N+1}=S_{1}$) when one applies Jordan-Wigner transformation to map the spin chain to spinless fermion chain, one needs to make sure in ...
2
votes
1answer
132 views

Symmetric potential well different solutions

I have solved $H|\psi\rangle=E_{n}|\psi\rangle$ with $V(x)=0$ from $-a<x<a$ and $\infty$ otherwise. If I propose a solution of the form $\psi(x)=A_{n}e^{ikx}+B_{n}e^{-ikx}$ I arrive to the ...
2
votes
1answer
25 views

Why are Cauchy boundary conditions an over-specification of boundary conditions for solving Poisson’s equation?

I was referred to Physics.SE by the following content published in Jackson’s Classical Electrodynamics: This rather surprising result [the fact that the potential within a charge-free volume is ...
1
vote
2answers
61 views

Proof that the momentum operator is hermitian without assuming the wavefunction approaches zero at infinity?

I am currently taking my second semester of quantum mechanics. For a number of proofs in the course, we have used the assumption that the wavefunction goes to zero at infinity. We have simply used the ...
4
votes
2answers
814 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}=\...
0
votes
2answers
186 views

Conducting cylinder by dielectric interface

To help me with a project I'm working on, I attempted to solve what I thought was an easy problem - There is an infinite, conducting cylinder of radius R at some potential V, located distance b from a ...
1
vote
0answers
43 views

If the lagrangian density changes by a total derivative of the lagrangian density

When we derive energy momentum tensor current by actively transforming field. We see that lagrangian ( density) changes by a total derivative of the lagrangian. If a total derivative of the function ...
0
votes
0answers
34 views

Finding the potential off axis of a uniformly charged disk

This is problem 3.22 from Griffiths We know the potential at any point on the axis perpendicular to the center of the disk, I'm asked to find the potential at any point $(r,\theta)$ assuming $r<R$ ...
3
votes
2answers
98 views

Diffeomorphic but physically inequivalent spacetimes

In the last few years there has been a considerable endeavor in understanding the asymptotic symmetries of quantum gravity on Minkowski Spacetime. This has been tied to a study of the BMS group that ...
0
votes
0answers
9 views

Derivation of driven force on a string. How to prove maximum amplitud is achieved at resonant frequency?

I know if I have a driven oscillator of natural frequency $\omega$, applying a driven force $F_0 \cos (\Omega t)$ will result in a motion equation like this one (steady state/particular solution): \...
0
votes
0answers
30 views

Boundary conditions for an infinite line charge and grounded conducing plane

I'm not asking for a solution to the problem, I'm confused about what I should set the boundary conditions to, it's obvious that $V=0$ at $z=0$ because of the grounded $xy$ plane, but I don't know ...
0
votes
4answers
2k views

Equation of reflected wave (fixed end/free end)

I have an equation of a wave as $y = 2 \sin\left( \dfrac{\pi}{6}x - \dfrac{\pi}{4}t \right)$. I want to find the equation of the wave which is formed when it gets reflected from (i) a fixed end or (ii)...
0
votes
0answers
39 views

Neumann boundary condition in spherical coordinates

I'm trying to solve heat equation $$\nabla^2 u = \frac{1}{k}\frac{\partial u}{\partial t}$$ in the region $$ a \leq r \leq b, \ \ \ \ 0 \leq \varphi \leq 2\pi, \ \ \ \ 0 \leq \theta \leq \theta_0 $$ ...
11
votes
3answers
7k 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: $$L = L(q, \dot{q}, \ddot{q},t).\tag{1}$$ If we're working on the variational problem for this Lagrangian, then I know that we'...
5
votes
2answers
2k views

Boundary conditions in Electrostatics

If I have a grounded conducting material, then I know that $\phi=0$ inside this material, no matter what the electric configuration in the surrounding will be. Now I have a conducting material that ...
2
votes
0answers
50 views

Dirac equation boundary conditions

In Schroedinger equation, which is second order differential equation, one normally, equates both $\psi(x)$ and $\psi'(x)$ across the boundary, as boundary conditions. However, the dirac equation ...
2
votes
2answers
53 views

Parallel plates capacitor, boundary conditions (paradox?)

Given a parallel plates capacitor with two dielectric as shown here: (dielectrics stacked in parallel). It's usually stated that the field is given by: $\vec{E}=\sigma/\varepsilon_i \hat{z}$ ...
2
votes
1answer
232 views

Governing equations and boundary conditions for a steady-state compressible viscous flow in an axisymmetric annular orifice

I'm trying to simulate a 2D axisymmetric model of steady-state compressible viscous flow using Mathematica, but I get some errors. There is a chance that I'm making some mistakes with the governing ...
0
votes
2answers
50 views

Closed end tube with anti-node

The experiment was about creating a sound wave inside a close ended resonance tube and finding the locations of maximum and minimum amplitude. (after adjusting the tube length that makes a standing ...
1
vote
1answer
48 views

Why does a wave reflect on the edge of an open tube? [duplicate]

Why does a wave reflect on the edge of an open tube? There is nothing solid to make the wave bounce. Then why is it reflected?
0
votes
1answer
376 views

Given total charge, how to calculate the surface-charge distribution

Suppose you given conductors $L_i$ with given geometry in space and the information that the conductor $L_i$ has the total charge $Q_i$ ($i = 1,\dots,n$). Suppose further that there are no additional ...
-1
votes
2answers
142 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 ...
2
votes
0answers
54 views

Conflict of domain and endpoints in Noether's theorem and energy conservation

In the derivation of energy conservation, there is the transformation $q(t)\rightarrow q'(t)=q(t+\epsilon)$, whose end points are kind of fuzzy. The original path $q(t)$ is only defined from $t_1$ to $...
1
vote
2answers
810 views

1D drift-diffusion equation with single absorbing boundary

If we have just the simple diffusion equation (in 1D): $$ \frac{\partial P(x,t)}{\partial t} = D \frac{\partial^2 P(x,t)}{\partial x^2} $$ with an absorbing boundary at x=0 and initial condition $P(x,...
0
votes
1answer
46 views

Do we need to specify additional conditions in order to find the unique potential satisfying Laplace's equation?

Let us say we have a simple boundary value problem (BVP) in spherical coordinates : $$\Delta \phi = 0$$ along with $\phi=1$ at $\,r=1$, and $\,\phi =0\,$ at $\,\infty$. A surface sphere with radius ...
0
votes
1answer
50 views

Current density boundary condition

Suppose that $$ {\nabla \bullet J= 0} $$ What I know about the boundary condition are for normal direction $$ J_{1n}=J_{2n} $$ for tangential direction $$ J_{1t}/\sigma_1=J_{2t}/\sigma_2 $$ ...
0
votes
0answers
13 views

What is the relationship between pressure and concentration in liquids in porous media?

I am working on a model in porous media. In particular, it is about the formation damage due to the precipitation. I assigned Dirichlet boundary condition for the concentration near the well-bore, ...
0
votes
0answers
87 views

Weak Solutions to the Einstein Equation across a Junction

Consider the principle part, i.e., the part which contains the highest derivatives of the metric (which is the $2^{nd}$ derivative) is $$\mathcal{P}\{R_{ab}\}=\frac{1}{2}g^{cd}\left(\partial_{a}\...
1
vote
2answers
73 views

Boundary conditions in QM and statistical physics

I don't understand something about boundary conditions in problem that I discuss it below. in QM we solve the particle in Potential well and we obtain that we should have $k=\frac{n*pi}L$ that $n\in{...
3
votes
3answers
2k views

Why don't E&M fields change orientation after hitting a surface?

In essentially every derivation of the Fresnel equations, the general problem of radiation hitting a surface at a certain angle is broken into two parts (out of which we hope the solution any general ...
5
votes
2answers
522 views

Boundary conditions in Poisson's equation for gravity

Say we want to calculate the gravitational potential everywhere around(outside) a solid, circular, right cylinder. We want to use Poisson's equation for gravity for that (Laplace(U) = -4*pi*density ...
7
votes
1answer
626 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 ...