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19 views

Is it true that $\frac{d}{dt}\int_S \mathbf{B} \cdot d \mathbf{a}$ goes to zero if the amperian loop $S$ contracts indefinitely?

I suppose to have an ordinary magnetic field: in the answer I'm not interested to involve Dirac delta: the integral goes to zero. I want to focus on another point: an infinitesimal physical quantity ...
0
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2answers
38 views

Particle in a box, quantization of energy

I'm learning about how the energy of matter is quantized like how the energy of light is. My textbook illustrates the concept of quantization with the particle in a box: "A particle of mass $m$ ...
1
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2answers
71 views

Derivation of Euler-Lagrange equation from principle of least action

When deriving the Euler-Lagrange equation for a field $\phi$ the term $$ \int\textrm{d}x^{\mu}~\partial_{\mu}\left( \dfrac{\partial \mathcal{L} }{\partial(\partial_{\mu}\phi)}\right)\delta\phi $$ is ...
6
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2answers
908 views

Question about the apparent loophole in principle of least action

In Lagrangian formalism, given two points $(x_1,t_1)$ and $(x_2,t_2)$, we ask the question which paths $x(t)$ make the action $S=\displaystyle \int_{t_1}^{t_2}L\ \mathrm dt$ stationary and satisfy the ...
1
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0answers
11 views

When light reflects from a medium of lower index of reflection to a medium of higher index of refraction, why does the light undergo a phase shift? [duplicate]

I learned in my physics class that there is a phase shift when light reflects off a low $n$ from a higher $n$, but never got the explanation.
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1answer
21 views

Can you have a problem with a Dirichlet boundary condition but with waves that reflect off the boundary?

Say we are looking for a solution to the Helmholtz equation $$(\Delta + k^2) u = 0,$$ in in the upper half space ($y > 0$) in 2D with a Dirichlet boundary condition on the $x$-axis, that is, $u(x, ...
6
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0answers
65 views

Is it possible to do a path integral between two boundaries analytically on a quantum lattice?

I have been trying to perform some path integral between two boundaries for a massless scalar field $$\int_{\varphi(t_a, \vec{x})}^{\varphi(t_b, \vec{x})} \mathcal{D}\varphi(x)e^{iS[\varphi(x)]}$$ ...
1
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3answers
70 views

Why don't E&M fields change orientation after hitting a surface?

In essentially every derivation of the Fresnel equations, the general problem of radiation hitting a surface at a certain angle is broken into two parts (out of which we hope the solution any general ...
0
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0answers
26 views

Problem with understanding boundary conditions in electromagnetism

In some books on electrodynamics they stress that electric current won't radiate if it is placed on a perfect electrical conductor (PEC), citing image theory: exactly opposite current will appear and ...
5
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1answer
68 views

Why are periodic boundary conditions used for the derivation of phonons? [duplicate]

I am currently reading "Quantum Field Theory for the Gifted Amateur". In chapter 2 Phonons are introduced as solutions (in k-space) of a coupled harmonic oscillator. In real space the oscillator is ...
7
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3answers
438 views

Interpretation of boundary conditions in time-independent Schrödinger equation

The time-independent Schrödinger equation: $$\ -\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + V\psi = E\psi$$ is second order, so we should expect the solution to have two "degrees of freedom" which can ...
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0answers
98 views

Why can we set the coefficient $c_- = 0$ in the solution of the quantum particle on a ring?

In the quantum particle in a ring problem, the general solution for the wavefunction, with $k = R \sqrt{2 m E / \hbar^2}$, $R$ being the ring radius, $c_{+, -}$ being constants, $E$ the energy, and ...
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0answers
18 views

Clarification of why pressure must be constant at a boundary between two fluids/gases?

In section 13.2.1 of these notes on acoustic waves it says that the pressure must be continuous at the boundary of two fluids/gases in equilibrium. If they were not it says the following - If the ...
1
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1answer
40 views

Correlating two definitions of bound states in quantum mechanics

In Griffiths, he defines a bound state to be that stationary state for which the total energy E is such that $E<V(\pm\infty)$. Let $\psi(x)$ is a stationary state satisfying $E<V(\pm\infty)$ and ...
3
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1answer
20 views

Suitable boundary conditions magnetic field paradox

Consider a point charge $q$ situated at the origin, and a uniform magnetic field, covering all of space, pointing in the $z$ direction $\mathbf{B}=B_0\hat{\mathbf{k}}$. What happens when you turn ...
0
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1answer
29 views

Boundary Conditions For Strings? [closed]

There seems to be two main boundary conditions for Strings. 1. Neumann Condition: Ends of Strings are free to move up or down. 2. Dirichlet Condition: Ends of Strings are fixed. What other ...
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0answers
18 views

When is the condition $V(x_i\rightarrow \infty)=0$ needed when solving the Laplace equation?

Im currently working on the solution of some Laplace Problems with Griffiths (Page 180). Often the condition $V(x_i\rightarrow \infty)=0$ appears when discussing problems of conducting plates, for ...
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0answers
25 views

Computing the value of an Action given some boundary conditions

Having being dealing with Actions for a while I have come across a question in which I am required to calculate the value for $S$ an action in the form of a function for some given boundary ...
2
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1answer
112 views

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 ...
4
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2answers
144 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 ...
2
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1answer
124 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 ...
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0answers
104 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 ...
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0answers
26 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 ...
0
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0answers
15 views

C.o.m. position and total momentum of open DD string

I'm trying to calculate c.o.m. position $q_\text{DD}^\mu$ and total momentum $p_\text{DD}^\mu$ of the open string with Dirichlet boudnary conditions on both ends. Something is going very wrong though. ...
1
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1answer
30 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 ...
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0answers
24 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 ...
0
votes
1answer
45 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 ...
3
votes
1answer
106 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, ...
1
vote
1answer
44 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 ...
15
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2answers
439 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 ...
3
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0answers
94 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 $ψ(x) → 0$ ...
1
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2answers
47 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 ...
3
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0answers
69 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. ...
1
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0answers
29 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 ...
3
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0answers
42 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 ...
0
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0answers
16 views

Incompressible Navier-Stokes boundary conditions

Let's say I have a unit cube $\Omega\in[0,1]^2$ where the inflow is on the left and outflow on the right, at the top and bottom boundary I have no-slip $u_1 = u_2 = 0$. At the inflow I prescribe ...
3
votes
1answer
66 views

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 ...
5
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0answers
140 views

on fundamental 2D conductivity equation boundary value problem

Consider the following homogeneous boundary value problem for a function/potential $u(x,y)$ on the infinite strip $[-\infty,\infty]\times[0,\pi/4]$ w/positive periodic coefficient/nductivity ...
1
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0answers
73 views

Why is the no-slip condition valid for fluids but not for solids?

You can obviously move a solid at a different speed along the surface of another solid, so how come the velocity of the fluid at the fluid-solid interface must be equal to that of the solid? What ...
0
votes
1answer
75 views

flat plate isoflux convection - how to calculate temperature

I am an engineer trying to design a simple 1D program for evaluating the temperatures of a multi-layer heatsink that includes convection and radiation heat transfer from the external surface. For a ...
0
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0answers
52 views

Infinite square well physical interpretation

In quantum mechanics, the description of the infinite square well is given with the potential energy defined as $$V(x) = \begin{cases} 0 & \text{if } 0 \leq x \leq a,\\ \infty & ...
0
votes
1answer
49 views

Boundary conditions and uniqueness of heat equation solution

I have some confusion about the uniqueness of solution in an unstable heat transfer problem. The domain of this problem is shown in the figure below, which is infinite in the left-right direction, ...
1
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2answers
85 views

Principle of least action and greedy algorithm

Is the principle of least action sort of a greedy algorithm that all mechanical systems follow?, sometimes to minimise and sometimes to maximise the quantity we call action, at each individual step.
0
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0answers
28 views

Cylinder in a magnetic field with its axis parallel to the field

Consider the case of a cylinder of some permeability $\mu$ in a constant external field. Now we are familiar with finding the scalar potential and $B$ for axis of cylinder being perpendicular to the ...
0
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0answers
49 views

Derivative condition in the Brachistochrone problem

I know that in general, to find the minimum of some line integral with given end points I need to solve E-L equations. what disturbs me is that I have seen in my class the famous Brachistochrone ...
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0answers
73 views

Derivation of open boundary conditions for Non-Equilibrium Green's Function (NEGF)

It is widely claimed that the Non-Equilibrium Green's Function (NEGF) equations for the study of quantum transport have been derived from the many-body perturbation theory (MBPT). Yet the bridge ...
10
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1answer
201 views

How to deal with boundary conditions for path integrals?

For non-relativistic quantum mechanics, the boundary conditions are rather simple to deal with, they are just \begin{equation} \langle x_1, t_1 \vert x_2, t_2\rangle = \int_{x_1(t_1)}^{x_2(t_2)} ...
0
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2answers
89 views

Difference for boundary condition, particle in a box

When solving the simple problem of a free particle in a box of volume $V = L^3$, we can impose either periodic boundary conditions $\psi(0) = \psi(L)$ and $\psi '(0)= \psi'(L)$ either strict boundary ...
0
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2answers
225 views

Vibrating string, free end boundary condition

When discussing the vibrating string problem with one end (or both) free to move in the vertical direction but constrained in the longitudinal direction (achieved by placing the "free" end in a ...
1
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2answers
173 views

Direction of H and B inside and outside a bar magnet

I seem to have encountered a contradiction when thinking about the directions of $\textbf{H}$ and $\textbf{B}$ inside and outside a bar magnet. Suppose that a bar magnet has a roughly constant ...