Questions tagged [boundary-conditions]

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605 questions
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Connection between black body radiaton and cavitys

I have some questions concerning the relation between the black body radiation and cavitys. First of all, i don't see, why you can derive the black body spectrum from the mode density of the ...
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Conservation of Noether current

In Peskin equation 2.12 $$\partial_\mu j^\mu(x) = 0, \quad {\rm for} \quad j^\mu(x) = \frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}\Delta\phi - \mathcal{J}^\mu$$ Why the current $j^\mu(x)$...
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Phase shift in reflection

Does every day-to-day life reflection cause a phase shift of pi? Or does this occur only in thin-film interferences?
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Periodic vs Open boundary conditions

In condensed matter, people often use periodic boundary conditions to perform calculations about bulk properties of a material. It's generally argued that in the $N\rightarrow\infty$ limit the ...
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Particle in 1D box. Different solutions for wavefunction

For a particle in a box $x$ ranging from $0$ to $L$ you get a solution of $\sqrt{2/L}\sin (n \pi x/L)$. But if you have a particle in a box $x$ ranging from $-L/2$ to $L/2$ infinite square well ...
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Numerical solutions with insufficient boundary conditions

Numerically is there a procedure to find at least one solution to differential equations given insufficient boundary conditions? For example: Consider electrodynamics in vacuum, and for initial ...
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Randomly initializing ensemble of particles in “toy” computer model

I'm programming a "toy" model, and want to intialize the $(\mbox{positions},\mbox{momenta})$ of an ensemble of particles in three-space, using a uniform (pseudo) random number generator. But I'm a ...
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Path integral defines a vector in Hilbert space

It is often stated that the path integral defines a state in the Hilbert space of the theory. I've seen this in low dimensional examples, with specific boundary conditions (for example paragraph 9.2 ...
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Why perpendicular component of Electric field is discontinuous across the boundary and parallel components continuous?

I was going through Griffith's electrodynamics boundary conditions and have a problem understanding the discontinuity of $E_\perp$ components. While deriving the electric field for an infinite sheet ...
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How can we justify $\psi(\textbf{r})\to\psi_{in}(\textbf{r})+\psi_{sc}(\textbf{r})$ at $|\textbf{r}|\to \infty$ but not at finite $|\textbf{r}|$?

In quantum scattering theory, the outgoing wave at $|\textbf{r}|\to\infty$, scattered from a localized potential, can be written as $$\psi(\textbf{r})\to\psi_{in}(\textbf{r})+\psi_{sc}(\textbf{r})$$ ...