Boundary conditions Definition and 364 Threads

Homework Statement Show that the conditions for a bound state, Eqn1 and Eqn2, can be obtained by requiring the vanquishing of the denominators in Eqn3 at k=i\kappa. Can you give the argument for why this is not an accident? Homework Equations Eqn1: \alpha=q*tan(qa) Eqn2...

Homework Statement Find the temperature distribution in the long thin bar −a ≤ x ≤ a with a given initial temperature u(x,0) = f(x). The side walls of the bar are insulated, while heat radiates from the ends into the surrounding medium whose temperature is u = 0. The radiation is taken...

Use Green's Functions to solve: \frac{d^{2}y}{dx^{2}} + y = cosec x Subject to the boundary conditions: y\left(0\right) = y\left(\frac{\pi}{2}\right) = 0 Attempt: \frac{d^{2}G\left(x,z\right)}{dx^{2}} + G\left(x,z\right) = \delta\left(x-z\right) For x\neq z the RHS is zero...

Homework Statement A thin conductor plate is in free space. Its conductivity is finite and thickness is approaching zero. Relate the tangential electric field in either side of the conductor. Repeat for tangential magnetic field. How are electric and magnetic fields related. Homework...

For a string fixed at x=0 and free at x=l I know \frac{dy}{dx}(l,t)=0 (d's are meant to be partials) but what is the other boundry associated with the end of the string? Is the second derivative also equal to 0?

I hope this is the right place to post this question. I'm trying to figure out how to run a numeric integration for a nonlinear second order ODE with Neumann B.C. I've started programming up Runge Kutta 4, but clearly without a boundary condition on the function, but only on its derivative...

Hey all, I finally figured out how to solve the integral: \int{dp} = \int{6U\eta(\frac{h-\overline{h}}{h^{3}})}{dx} + C using maple and have it export to MATLAB where: h=R+h0-\sqrt{R+x}\sqrt{R-x} \overline{h}=R+h0-\sqrt{R+\overline{x}}\sqrt{R-\overline{x}} how do i find the...

Could someone plase hep me with normal coordinate substitutions with periodic boundary conditions, I can't see where the 1/N cancels in the attached file Thanks Doug

Hi friends, I'm new to CST microwave studio. Just finish constructed a structure of an L-probe patch antenna (from IEEE paper) and just run the simulation by transient time solver, the curve of the return loss(S11) against frequency that i get is different from what showing on the IEEE paper...

\frac{dN}{dt}=-k_sN^2 Attempt: \frac{1}{N^2}dN = -k_s dt Integrate: -\frac{1}{N} + C = -k_s t In the solution manual, C is written \frac{1}{N_0} Why?

I'm reposting this because there was a problem with the title/LaTeX last time. Homework Statement Solve the wave equation (1) on the region 0<x<2 subject to the boundary conditions (2) and the initial condition (3) by separation of variables.Homework Equations (1) \frac{\partial^2...

Though this question arose in quantum mechanics, i think it should be posted here. Consider a particle in a well with infinite walls: $i i \frac{\partial \Psi}{\partial t} = -\frac12 \frac{\partial^2 \Psi}{ \partial x^2},\:0<x<a$ but the wall start to squeeze :devil: $\Psi(x=0,t) \equiv...

Homework Statement Homework Equations N/A The Attempt at a Solution Really stuck with this, i can't work out how to apply the boundary conditions to generate the simultaneous equations to find the specific solution. Can't find any similar examples either. Help appreciated.

Homework Statement Homework Equations N/A The Attempt at a Solution The problem and attempt are as above, I'm not sure where to go from here though. I'm not sure what to do with the boundary condition of dx/dt=-2 and t=0. Any help appreciated.

what do boundary conditions mean wid respect to transmission lines??

Homework Statement Hi all. I have the following expression, which relates the incoming amplitude with the reflected amplitude at a point x = L in a coaxial cable: A_{\text{reflected}} = \frac{R-Z_0}{R+Z_0}A_{\text{incoming}}. Here R is the resistance at the point x = L and Z0 is the...

Homework Statement One half of the region between the plates of a spherical capacitor of inner and outer radii a and b is filled with a linear isotropic dielectric of permittivity \epsilon_1 and the other half has permittivity \epsilon_2, as shown in the figure. If the inner plate has total...

Hi, I have been given a differential equation to use in order to solve for the Hydrogen wavefunction in the ground state using Euler's method. d^2u_nl/dr^2 -(l(l+1)/r^2)*u_nl + 2k*(E_nl-V(r))*u_nl = 0 V(r) = -a/r where a = 1/137.04 I have been given initial conditions u_nl(0) = 0 an...

I am trying to solve an ode of the form u"(x)=a(x) where a(x) is some known function and the domain is from -inf to +inf. I am required to use Green's function. The boundary condition is u(0) = Integral[u(x),{x,0,1}] = 0 My Green's function has the form G(x,y) = A(y)*x+B(y) x<y G(x,y)...

Homework Statement Calculate potential function and the electric field for the region between two concentric cylinders, where V ( inner cylinder) = 0 at r = 0.015 m and V(outer cylinder) = 100 for r = 0.025 Homework Equations \Delta (square ) V = 0 The Attempt at a Solution so...

Hi. You know that B_{1n} = B_{2n} as one of the boundary condition when magnetic field is go across from material 1 to material 2, n means direction perpendicular to the boundary surface. I wander this theorem is right in non-uniform field which is function of space variable r...

Firstly I really feel so lucky to find this forum. Since I don't have a strong physics background but now dealing with many problems directly related to physics. I'm now doing some simulation in comsol and need to solve some PDEs. I'm using this PDE coefficient form in comsol. The equations...

Homework Statement Hi all. I am given the following differential equation: X'' - k*X=0. I am told that k = -m^2, so the general solution is given by: X = a*cos(m*x)+b*sin(m*x), where a and b are constants. I am also given boundary conditions: 1) X(-Pi) = X(Pi) 2) X'(-Pi) =...

Homework Statement Solve Laplace's equation inside the rectangle 0 \le x \le L, 0 \le y \le H with the following boundary conditions u(0,y) = g(y)\text{, } u(L,y) = 0\text{, } u_y(x,0) = 0\text{, and } u(x,H) = 0 Homework Equations The Attempt at a Solution I know that with...

Free Electron Model: Why periodic boundary conditions and what is "L"? Right, hello! The quantum free electron model for electrons in solids (in One dimension) says we need to use periodic boundary conditions such that if Y(x) is the wavefunction, then Y(x) = Y(x+L). Where L seems to be...

Mods: I wasn't sure if I should put this here or in DE's, if you think it would be better there, feel free to move it. Everyone: If I have a bunch of particles, which I'm modelling as a continuum, and I want to put periodic boundary conditions which reflect (completely specular reflection)...

Hey folks, I'm trying to find the Green function for the equation -\partial_\mu \partial^\mu \phi = K where K is some source term. Its a 2D problem with the wave confined to a rectangular cavity where the cavity is located at z = 0 and z=a. This tells me that G|_0= G|_a=0 I've pretty...

Hey people can u please tell me what will be the boundary conditions for a circular plate with a central hole clamped at the circumference... Plate is axis symmetric and is under uniform load..

What are the general boundary conditions for nonviscous, incompressible fluid flow? I am trying to find the velocity of fluid at the surface of a sphere with the incident fluid having uniform velocity. I am surprised to find in the solution that the radial velocity at the surface does not...

I can't understand this conditions, and in general every boundary conditions for problems like this. they states "the choice of boundary conditions can be determined by mathematical convenience (!?) ... for if the metal is sufficiently large, we should expect its bulk properties not to be...

Hello friends, Thanks in advance for your answers, I am using genreal form of PDE to solve system of PDEs. I am dealing with cyllindrical co-ordinates under axisymmetric case. I am not able to understand how to implement boundary conditions such as, DEL. Gamma=F is system of PDEs where...

Hi I'm trying to solve a magnetostatic problem and I'm not sure which boundary conditions must be applied to the magnetic vector potential (A) on magnetostatic problems? Thanks in advance.

Hey all, I'm wondering if someone can help me understand how to apply the boundary conditions to the diffusion equation in one dimension. Diffusion equation is: \frac{\partial u}{\partial t}=D*\frac{(\partial)^{2}u}{\partial x^{2}} The initial condition is: u(x,0)=0 And the boundary...

Hello hello, I cannot for the life of me wrap my head around the idea of a boundary condition. I understand the idea (at least I think I do) of solving a differential equation with given initial conditions. But is solving for a magnetic field or electric field while enforcing...

Hey guys, just need some hints with this doosey Homework Statement We have (x^2 y')' + ax^2y = 0 where a the eigenvalue (a sturm-lioville problem) (sp?) with y'(0)=y(1) = 0 and we get the hint to substitute f = y/x. The Attempt at a Solution Ok so i get the general solution being a sum of...

If I have a finite boundary, say of length L. Is it possible to demonstrate that if I were to allow all possible CONTINUOUS values of a wave to exist (with unit amplitude) then deconstrutive interference destroys all waves except those with wavelength: k=\frac{n\pi}{L} Where n =0,1...

One thing that's always bothered me about Bloch's theorem is the periodic boundary conditions which are imposed on the system. Clearly, when dealing with an actual solid, the more natural choice would be to impose zero at the boundaries. I know that periodic conditions make the math easier, but...

I wasn't completely sure where to put this (programming or Diff.E.'s), so if there's a better place, maybe the mentors could move it for me. I'm doing some numerical simulations involving the (2-D) wave equation, and was wondering if anyone could tell me (or give a reference to a paper which...

solve the next differential equation: y´´- a*y= \delta (x-d) with the boundary conditions: \left.\frac{\partial y}{\partial x} \right|_ {x=0} = 0 lim _{x\rightarrow\infty} y = 0 I get the homogeneous solution: y_H = C_1 exp (\sqrt{a}x) + C_2 exp (-\sqrt{a}x) and then to...

Hi, I'm trying to find an analytical solution of Laplace's equation: \phi_{xx} + \phi_{tt} = 0 with the tricky boundary conditions: 1. \phi(x=0,|t|>\tau)= 0 2. \phi(x\neq0, |t|>>\tau)=0 3. \phi_{x}(x=0, |t|<\tau)=-1 4. \phi_{t}(x, |t|>>\tau)=0 I have the following ansatz(I...

what do mean the author by the red underline line? http://img164.imageshack.us/img164/7404/contfv6.jpg Why would 33.22abe false? Thanks.

Homework Statement What is the stationary (steady state) solution to the following reaction diffusion equation: \frac{\partial C}{\partial t}= \nabla^2C - kC Subject to the boundary conditions C(x, y=0) = 1, C(x = 0, y) = C(x = L, y) (IE, periodic boundary conditions along the...

Hi to all community of Physic's help from Florence, looking at born-von karman BC I'm a bit confused. I put this condition when i assume periodicity of wave function where the period is the spatial dimension of my system. I found that BC first in solid state physic, then I've noticed that...

Hi, Can anyone please tell me how to go about solving this system of coupled ODEs.? 1) (-)(lambda) + vH''' = -2HH' +(H')^2 - G^2 2) vG'' = 2H'G - 2G'H lambda and v are constants. And the boundary conditions given are H(0) = H(d) = 0 H'(0) = omega * ( c1 * H''(0) + c2 * H'''(0) )...

Hi I am new to solid state. I just read about fermi gas in a cube. For some reason the author used periodic boundary conditions? Why didn't they choose finite well potential where the height of the well is related to the work function?

I need help figuring out the solution to this diff.eq. y(x) = x + (1/2)*∫(from u=-1 to 1)[ ( 1-| x – u | ) y(u) du] , x є [ -1, 1] I have to show that: y``(x) + y(x) = 0 , x є [ -1, 1] subject to: y(1) + y(-1) = 0 y`(1) + y`(-1) = 2 Thanks for any help you can give.

Homework Statement The edges of a square sheet of thermally conducting material are at x=0, x=L, y= -L/2 and y=L/2 The temperature of these edges are controlled to be: T = T0 at x = 0 and x = L T = T0 + T1sin(pi*x/L) at y = -L/2 and y = L/2 where T0 and T1 are constants...

how do you prove/show that there really is a vector space defined by certain boundary conditions? unfortunatly this part of pde's was glossed over in my professor's lecture notes and I don't recall him talking about it in class.

I have done most of a question except for the most important part, putting in the boundary conditions, I can't really interpret them. The question is: I managed to solve this, with -c^2 as a separation constant, and I got: T(x,t) = X(x)F(t) = (A_{1} \cos{\frac{cx}{\sqrt{\kappa}}} + A_{2}...

Hey all, Last year, I took my university's undergraduate QM sequence. We mainly used Griffiths' book, but we also used a little of Shankar's. Anyway, I decided to go through Shankar's book this year, in a more formal treatment of QM. After the first chapter, I already have some questions that...