Questions tagged [boundary-conditions]

The tag has no usage guidance.

605 questions
18 views

How can we predict how a system evolves using the stationary action principle even though we need to specify the final state? [duplicate]

The stationary action principle states that a system evolves between a fixed initial and fixed final configuration in such a way that the action is stationary. But isn't the final configuration what ...
56 views

Green's function for infinite square well

The Green's function can be given in terms of left and right solutions. $G(x,x';k) = \frac{1}{W}\left(\Psi_{L}(x_{<})\Psi_{R}(x_{>})\right)$ But I don't understand how to determine these left ...
24 views

Intuition for construction of a wave reflected from a general corner reflector

Consider a corner reflector with angle $\alpha$ between its semi-planes: Let a plane wave come from the bottom into this reflector (possible at an angle). The objective is to find the total wave ...
46 views

How is Poisson's Equation solved numerically?

This question is of pure interest. I would like to know, how a mixed boundary value problem like the following can be solved numerically: Lets say I have two conducting plates (not necessarily ...
89 views

24 views

Boundary conditions for backscattering?

In solving the well-known problem of normal incidence reflection, it is typical to say that there should be no backwards-moving wave on the far side of the reflective surface, or in other words that ...
24 views

Switching between advanced and retarded solutions mid-integral?

In wave mechanics, an advanced solution can be thought of as a wave that propagates until it is "caught" and stopped by the forcing function, and a retarded solution can be thought of as a wave that ...
306 views

113 views

Boundary conditions for calculus of variations in phase space and under canonical transformations

This might be a stupid question, but I just don't get it. In Hamiltonian mechanics when examining conditions for a $(\boldsymbol{q},\boldsymbol{p})\rightarrow(\boldsymbol{Q},\boldsymbol{P})$ ...
36 views

Property of surface Green function in electrostatic field

Let's consider a 2D-square with 4 equal subsquares containing different dielectrics. Inside the square domain, the unknown electric potential function $\Phi$ satisfies the Laplace equation: \nabla^...
67 views

Boundary condition: displacement

I have a controversial case. I have a rod, which is fixed from one end (constraint). From another end, I apply a compressive force, by pressing the rod down. So in a way I have a constraint, but at ...
135 views

Noether's Theorem, Boundary-Bulk, and Open Thermodynamic Systems

Before going any further, I should emphasize that I know we cannot use the action principle for locally dissipative systems or even Noether's theorem for that matter. There are plenty of stackexchange ...
206 views

Difference between bound and free charge/current in a perfect conductor

For the case of charge, it seems clear that in a perfect conductor the free charge refers to the excess charge that has been dumped into the conductor, while the bound charge refers to the charge that ...
68 views

If the path integral formulation includes future events, why doesn't that imply retrocausality?

I know that such events would cancel out in the math, but if an extreme event were to happen in the future (say a black hole forming or something on that par), would a particle in the present react to ...
1k 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)...
42 views

Confusions about Israel's paper on junctions / singular shells in GR

After reading Israel's well-known paper superficially (see also the erratum) I thought that his formulas (38)-(40) were necessary and sufficient conditions to join two manifolds along a time-like ...
2k views

How can the solutions to equations of motion be unique if it seems the same state can be arrived at through different histories?

Let's assume we have a container, a jar, a can or whatever, which has a hole at its end. If there were water inside, via a differential equation we could calculate the time by which the container is ...
151 views

On the boundary conditions for closed and open strings

In the process of finding the equations of motion for a string from the Polyakov action (say in the conformal gauge), we have to implement some boundary conditions on the target spacetime coordinates \$...