# Questions tagged [boundary-conditions]

This tag is for questions regarding to the boundary conditions (b.c.) which expresses the behaviour of a function on the boundary (border) of its area of definition. The choice of the b.c. is fundamental for the resolution of the computational problem: a bad imposition of b.c. may lead to the divergence of the solution or to the convergence to a wrong solution.

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### Boundary-condition-changing Operators for Free Boson BCFT with Dirichlet Boundary Conditions (or more general BCFTs)?

Is there any literature about boundary-condition-changing (b.c.c.) operators for the Free Boson with Dirichlet Boundary Conditions? The b.c.c. operators I'm interested in would replace boundary ...
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### Eigenstates of the Laplacian and boundary conditions

Consider the following setting. I have a box $\Omega = [0,L]^{d} \subset \mathbb{R}^{d}$, for some $L> 0$. In physics, this is usually the case in statistical mechanics or some problems in quantum ...
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### Electromagnetic Field in a 3D Cavity with Lossy Boundary

I would like to find the electric and magnetic fields inside a cubic cavity with a lossy boundary (i.e. NOT a perfect conductor). I assume that the interior of the cavity is filled with a homogeneous ...
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### Static pressure vs ambient pressure

If in a real scenario, a flat surface with a flush perpendicular closed duct of small diameter is exposed to a tangential fluid flow(laminar and naturally with the presence of boundary layer effect), ...
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### Boundary conditions for the stagnation point axisymmetric boundary layer equations

Good morning, I am trying to solve the Boundary Layer equations in the stagnation point in order to compute the stagnation point heat flux. In particular, the fluid is: -A continuum -In thermal and ...
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### On the validity of energy eigenvalues obtained when solving the Schrödinger equation for a particle in a 1D box

I'm having trouble understanding the legitimacy of solving the Schrödinger equation for a particle confined in an infinite square well. Aren't we supposed to solve it for the whole space and not just ...
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### Wigner's formula for the kinetic energy density in QM

In the Schroedinger equation the kinetic energy is represented by the operator $T = -\frac {\hbar^2} {2m} \Delta$ which acts on a wavefunction $\Psi$. If we multiply this by the complex conjugate of ...
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### Boundary Conditions for Spherical Harmonics Problem

I have encountered a problem with electrostatics potentials. The problem is given as follows: A sphere of radius $𝑎$ has the potential $\Phi(a,\theta, \phi)$ at the boundary. Obtain expressions of ...
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### Identification of the variation on the boundary and why $\delta S_{\partial V}=0$

I recently asked this question about variational principles and how it all works. The essential answer I got was to go read a book on the calculus of variations, which I did, and this helped me make ...
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### Boundary for 2D Laplace equation in electrostatics

I'm currently delving into the fascinating topic of electrostatics, specifically the distribution of potential in configurations involving conducting plates and charged wires. My focus is on a setup ...
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### How to understand variational principles and the math underlying them? [duplicate]

I work in finance, and studied math in college. I'm trying to use QFT statistics to model some aspects of the market. (I've already made some progress by deriving the Black-Karasinski Hamiltonian for ...
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### Frequency, if any, of a string with two different thicknesses [closed]

Very brief question. Assume a string that is made half out of a thin rope and half out of a thick rope (the thick rope is heavier of course). A transverse mechanical pulse is applied at one end (...
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### Terms in the Israel Junction Conditions

I'm confused about the Israel Junction Conditions. I've seen them written several different ways so far, but here I'll use: $$K^-_{ij}-K^+_{ij}=8\pi(S_{ij}-\frac{1}{2}g_{ij}S).$$ My understanding is ...
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### Is this image on harmonics and overtones wrong?

I saw this image and believed this to be the definition of what the relationship between harmonics and overtones to be in strings, closed pipes and open pipes. That the $n^{th}$ harmonic = $n-1^{th}$ ...
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### Fermion boundary conditions vs projective representations

I have a basic confusion about the two different boundary conditions for a fermion around a compact direction, periodic versus anti-periodic. We learn in a QM class that a fermion wavefunction picks ...
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### In Rayleigh-Jeans radiation law, why are the values of $n$ taken to be non-positive only?

In $k$-space the allowed values for standing waves in a cube of side length $L$ are given by $$\vec{k} = \left(\frac{\pi}{L}\right) (n_1, n_2, n_3)$$ where the $n_i$ are nonnegative integers. Why are ...
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### Fourier transformation of Hamiltonian with Alternate Hopping amplitude

How to perform the Fourier transformation of the series: $$\sum_{<l,m>}(-1)^{l+1}(a_{l}^{+}a_{m}+a_{l}a_{m}^{+})$$ where the sum is over the nearest neighbours (l,m), l=1 to N,and there is ...
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### Where did the idea for the approach to solving this boundary layer problem come from?

I found the derivation of Blasius-Equations here: A free stream velocity hits a flat plate and the goal is to derive boundary layer behavior. Everything in this tutorial is clear - but the most ...
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