# Questions tagged [boundary-conditions]

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### Minimizing the Lagrangian action of an impossible problem

I'm working my way through Structure and Interpretation of Classical Mechanics (SICM), and am stuck on an exercise in Section 1.4: Exercise 1.6. Minimizing action: Suppose we try to obtain a ...
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### Current Density Boundary Conditions and its Implications

According to Ohm's Law, one can say $\overline{J} =\sigma \overline{E}$ if the field is in a conductor, and $\overline{J} =0$ if it's in empty space. Now if we take the surface of a conductor and ...
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### Can Ampere's Circuital law be used on an infinite number of alternating Helmholtz coils?

I have the following surface current density $$\bar{\sigma}_s = \hat{\phi} \sin(kz) |\bar{\sigma}_s|$$ to approximate an infinite number of alternating Helmholtz coils stacked along the z-axis with ...
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### Boundary conditions of the radial Schrodinger equation

Consider the radial differential equation $$\bigg( - \frac{d^2}{dr^2} + \frac{(\ell+\frac{d-3}{2})(\ell+\frac{d-1}{2})}{r^2} + V(r) + m^2 \bigg) \phi_\ell (r) = \lambda\ \phi_\ell (r),$$ which I've ...
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### Why do electric field lines start and end at 90 degree at the surface of a conductor? [duplicate]

There is one property of electric lines of forces which states that: Electric field lines start and end at 90 degree at the surface of the conductor. But why is that so? Is there any proof for ...
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### Newton's law of cooling for the heat equation boundary condition

Newton's law of cooling says the temperature of an object satisfies $$\frac{dT}{dt} = -k(T(t) - T_0),\tag{1}$$ where $T_0$ is the surrounding temperature. See these HTML notes for example. Now if ...
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### Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain?

Let $\Omega$ be a domain in $\mathbb{R}^n$. Consider the time-independent free Schrodinger equation $\Delta \psi = E\psi$.[*] Solutions subject to Dirichlet boundary conditions can be physically ...
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### Why do we not require higher derivatives to match at boundary when solving the Schrödinger equation in a given potential?

When solving the time independent Schrödinger equation for a given potential in 1D, the main part of the solving involves matching boundary conditions. Usually, we require the value and the first ...
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### How do i mathematically represent reflection in a (diffusion) Problem?

I am trying to formulate boundary conditions and it occurred to me that I never had to implement a reflective boundary before. The example is a one dimensional diffusion, where at $x=0$ the ...
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### Fourier series for a wave on an infinite string?

From "Vibrations and Waves" by A.P. French I know that any wave on a string length $L$ can be represented by: $$y(x,t)=\Sigma^\infty_0 A_n \sin(\frac{n\pi x}{L})\cos(\omega_nt-\delta_n)$$ But can we ...
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### When does $\mathbf n\times(\nabla V_2-\nabla V_1)=0$ imply $V_1=V_2$

I was reading a paper on electrohydrodynamics which has the following sentence (in my own words): At the interface/boundary, the requirement of continuity of the tangential component of the ...
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### Phase change by reflection [duplicate]

Let's consider a light ray falling on a cuboid made of glass at the angle $\alpha$. Then there will be a reflected ray $A$. The ray will also refract. Let the refracted ray be $B$. Ray $B$ will be ...
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### Reflection of Sound wave (Pressure Wave)

I want to study about the phenomenon of reflection of pressure waves as in an open ended organ pipe. Please suggest a suitable resource? I know about the harmonics in a stretched string and I can use ...
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### Could you give boundary conditions to the gravitational potential given the density distribution?

We´re doing a project that's all about solving differential equations with separation of variables. We´re trying to find the gravitational potential given the density distribution (that has azimuthal ...
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### How to specify boundary conditions as function of curvature in dynamic elastic beam pde?

In this article (already mentioned in this question) the dynamics of a planar elastic beam with "cantilever constrains" (one clamped end and one free end) is modeled. Using the Euler-Bernoulli Beam ...
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### How come a current sheet of $J_s = J_0 \hat{x}$ produces plane wave solution?

Given in the picture. There is a current sheet $J_s = J_0 \hat{x}$. Supposedly Jo is not oscillating. So, how does this thing create a plane waves propagating away from the current sheet? Shouldn't ...
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### Zero stress boundary conditions for the acoustic wave function

When is it appropriate to use zero normal stress boundary conditions when solving the acoustic wave equation. That is when the pressure is equal to zero.
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### Solving inhomogeneous differential equation with Green function

I'm not sure if this question is for physics forum, but my book's title is "Green's Functions in Quantum Physics", so I ask here. The book says that the Green's function defined as  (z-L( \mathbf{...
Background Consider a non-relativistic particle in a one-dimensional box of length $L$ with (for definiteness) an attractive delta function at the origin: \$H = \frac{P^2}{2m} -|c|\delta(x), \qquad 0&...