# Questions tagged [boundary-conditions]

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### Conditions to determine the Green's function for scattering phenomena

Consider the elastic scattering of particles by a potential $V$ in Quantum Mechanics. In the zone of influence of the potential the Hamiltonian may be written as $$H = H_0 + V,$$ being $H_0$ the ...
301 views

### Missing Hypothesis in Electromagnetism Texts

In the Feynman Lectures, Chapter 21, I find the statement We have solved Maxwell's equations. Given the currents and charges in any circumstance, we can find the potentials directly from these ...
499 views

### Is every solution of Einstein field equations unique?

Einstein's equation is $$8 \pi T_{ab} = G_{ab},$$ where the left side contains the stress-energy tensor and the right side contains the Einstein tensor. Is there exactly one unique stress-energy ...
134 views

### What is the exact value of the constant in the similarity solution for blast waves?

Recently I used the Rankine-Hugoniot equation to reason that the limit of the speed of shock waves for extremely strong shocks is $\bigl(\frac{6P}{5r_0}\bigr)^{1/2}$ where $P$ is the pressure of the ...
436 views

### Standing Waves in a String of two Linear Densities

Given a string with sections of two linear densities like this: Does the point where the two linear densities meet have to be a node if a standing wave is produced? Are there alternatives? Could I ...
45 views

### Normalization of states of continuos spectra with complicated boundary conditions

Let's consider the following Schrödinger equation: $$\psi''(x)+k^2\psi(x)=0$$ with the following boundary condition $$\psi(0)+a\psi'(0)=0$$ $k$ is supposed to be larger that $0$. This equation is ...
82 views

### Perodic boundary conditions vs Dirichlet?

I have been working through several examples recently involving particles in boxes (when finding the partition function of an ideal gas for example or looking at photon gases). I have seen two ...
60 views

### Size of box vs. discrete-ness of state of the system

From Statistical Physics, 2nd Edition by F. Mandl, pg. 36: A sufficiently large box (say 10 light-years across) will clearly not affect the properties of our system, ion plus electron sitting ...
130 views

### Why doesn't $σ_xσ_p$ change with the width of the well in the infinite square well problem (intuition)?

I calculated that the product of the uncertainty in position $\sigma_x$ for the ground state of an infinite square well of width $L$ with the uncertainty in the momentum $\sigma_p$ for the same state, ...
139 views

### Problem with boundary condition for the differential equation of a cooling Cube and Sphere

Lets considere a sphere of radius $R$ in a temperature $u_0$ which is cooling in an environment of temperature $u_\infty$ (Note: I already solved it). I have to solve a diferential equation and one of ...
3k views

### Stokes theorem in Lorentzian manifolds

I've fallen accross the following curious property (in p.10 of these lectures): in order to be able to apply Stokes theorem in Lorentzian manifolds, we must take normals to the boundary of the volume ...
224 views

### Eigenvalue problem $−\psi''(x) − (ix)^ N \psi(x) = E\psi(x)$ in complex plane

To find the eigenvalue in the complex plane of $x$ for one dimensional Schrodinger equation $$−ψ''(x) − (ix)^ N ψ(x) = Eψ(x).$$ where $N$ can be any real number, the boundary condition $ψ(x) → 0$ ...
83 views

### Could someone please explain the physics as to why two trash-bins could be more stable if placed together instead of apart during windy conditions?

I recently asked the following question on another StackExchange community(Home Improvement: Preventing trash bins from falling by placing apart of side-by-side, on a windy day?), but I would like ...
554 views

### What is the electric field exactly on the surface of a conducting sphere?

Within a conducting sphere, the electric field is 0, but is the electric field still 0 exactly on the surface?
551 views

### Why must this boundary condition be met? (Electromagnetic wave at interface between two mediums)

My textbook says that The laws of Electromagnetic Theory (Section 3.1) lead to certain requirements that must be met by the fields, and they are referred to as the boundary conditions. ...
234 views

### (boundary conditions) Interface between two lossless media

I'm wondering why there's usually no free charges nor free currents in the interface between two lossless media? no free current "I guess" is due to the insulating nature of a lossless media but why ...
78 views

### “Simple” Variation of the gravity action with boundary

I'm concerned with the derivation of the quasi-local stress tensor (getting from eqn 2.4 to eqn 2.6 in this paper: http://arxiv.org/abs/hep-th/0508218). As is the case with all the references I have ...
### Solved Gauss' Law for $\vec{E}$ without boundary conditions?
Why can I solve for the electric field of a point charge Q at the origin without boundary conditions? $\nabla\cdot\vec{E}=\rho/\varepsilon_0 = \delta(\vec{r})/\varepsilon_0$ is a 1st order ...