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Questions tagged [potential]

Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the potential-energy tag.

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Sphere half-submerged on a dielectric

This is a classic problem in electrostatics with a twist, so I thought it could be useful for others here. I did have a problem with the integration at the end, but on general I think the idea can ...
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155 views

$D$-dimensional Schrodinger's equation with a Dirac delta potential

I know that for $D\geq 2$, there is no bound state for a Dirac potential $V=-\alpha \delta(\textbf{x})$ unless we use an ultraviolet cutoff $k_{max}=1/a$. I showed this by solving the Schrodinger's ...
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173 views

Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
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60 views

Maxwell theory : How to justify the potential gauge fields if there are magnetic monopoles?

Without magnetic monopoles, the Maxwell equations are these (I'm dropping vector notations and all constants, for simplicity): \begin{align} \nabla \cdot E &= \rho_{elec}, \tag{1} \\[12pt] \nabla \...
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107 views

What is a good analogy for electric potential?

When the electrical field was defined I could totally relate to $\vec{E}$ being like $\vec{g}$ in mechanics. But for the electric potential I don't know what would be equivalent analogy. Any ...
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How to derive the simplest 1D Superpotential Hamiltonian?

In the superpotential wiki article there are definitions of two supersymmetric operators: $$Q_1=\frac{1}{2}\left[(p-iW)b+(p+iW)b^\dagger\right] \\ Q_2=\frac{i}{2}\left[(p-iW)b-(p+iW)b^\dagger\right] $$...
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could a force with corolios and centrifugal terms be written as a potential gradient?

I have an exam in classical mechanics next week, so I came across this problem which I did not fully understand nor any of my colleagues (it was a bonus problem in an old exam) I just want some hint ...
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305 views

Accelerated ion beam current

If an electron gun creates a $10\space mA$ electron beam and each electron collides with a gas atom and creates an ion through impact ionization, can the ions then be accelerated with a separate ...
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Conservation of momentum in statistical physics in presence of a potential

Imagine a number of particles, all confined in a parabolic potential. The particles initially have a random velocity and are let free to bounce off each other (say, it's rigid spheres). Does ...
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123 views

Is the “Force” of Gravity Simply Hamilton's Principle on a Curved Spacetime?

It's my understanding that General Relativity abstracts away the concept of gravity as a force, and instead describes it as a feature of spacetime by which massive objects cause curvature. Then it ...
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Charge distribution and potential in a 1-dimensional quasistatic system

Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution $\rho(...
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407 views

Symmetries of separable potential

For separable potential, say $x^4+y^4$, its symmetry are degenerate. Is that a generic case to every separable potential? I will explain my question: The potential $x^4+y^4$ has $A_1, B_1, A_2, B_2, ...
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27 views

Would the voltmeters give different readings in a circuit with induced current?

$\def\vE{{\vec{E}}}$ $\def\vD{{\vec{D}}}$ $\def\vB{{\vec{B}}}$ $\def\vJ{{\vec{J}}}$ $\def\vr{{\vec{r}}}$ $\def\vA{{\vec{A}}}$ $\def\vH{{\vec{H}}}$ $\def\ddt{\frac{d}{dt}}$ $\def\rot{\operatorname{rot}}...
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66 views

What does it mean for a potential not to have a Fourier transform?

Consider an isotropic potential $\phi(r)$ corresponding to the classical force of interaction between two point-particles. The Fourier transform of this potential $$ \Phi(k) = \int \exp(-i\vec k\cdot\...
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Multipole expansions: test on a function $\zeta=\zeta(t)$

Considering the potential $\psi(r)$ of a sphere of mass $M$ with density $\rho(\mathbf r')$, connected by a small volume positioned in the $P'$ point as shown in the figure: The $\psi(r)$ is: $$\...
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90 views

Which test function (under variational method of approximation) should be used for a linear potential?

There is this problem, it is not for evaluation, I mean, it is not homework. There is a 3-dimension potential $V(r)=C . r$, where $r$ is the radial coordinate and $C$ is a real constant (I think it ...
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Vector potential of a partially-known magnetic field

let's consider a three-dimensional space permeated by a known magnetic field $\vec{B}$. Let's consider in this space a topologically spherical surface $\mathcal{S}$ centred in the origin. I put a ...
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The formula for the average number of fermions $\langle N \rangle$

In the context of Fermi gases (or fluids in general), one would typically in the grand-canonical formalism use the formula $\langle N \rangle = -\frac{\partial \psi}{\partial \mu}$, where $\psi$ is ...
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171 views

Standing spherical wave solution

Let's say we have a spherically symmetric light wave $u(r,t,\theta,\phi)= u(r,t)$ that satisfies the following wave equation with spherically symmetric potential $V(r)=2/r^2$ (also set $c= 1$ so $\...
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68 views

What if in potentiometer, the loops are not balanced to cancel the potential and current flows?

As described in the book (image) that loops should be balanced with equal potential with help of the galvanometer. What if the we do not balance it to zero and have some current flowing? Can we still ...
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173 views

Derivation of Feynman Rules for a $\frac{1}{\phi}$ potential

The question is more mathematical in nature. If one had a potential $V(\phi) = \frac{\lambda}{\phi}$, where $\lambda$ is a constant, then how does one derive the Feynman rules for this scalar field's ...
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Dirac Delta potential and perturbation

I have a Dirac Delta potential as follows : $$V(x)= - \alpha \delta (x)$$ I know how to solve that problem. There is exactly one bound state. Now let's say I have an initial wave function in this ...
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871 views

Solving the Poisson equation using Green's function

Edit: should I perhaps post this question at math.stackexchange? It seems to me that physics maybe isn't really the right place for it, as it is more about mathematical methods. I have the following ...
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Guess the wave function in a given potential

Are there any techniques in guessing the ground state wave function in any given potential? For example, for a given potential like $$ \frac{1}{1-x^2}$$ or $$ \frac{1}{1-x^3}~?$$ I know wave ...
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Gauge Permitting c Magnetic Vector and Instant Electric Scalar Potentials?

The Lorenz gauge requires c propagation of both scalar and vector potentials. The Coulomb gauge requires instant "propagation" of these potentials but is stated in such a way as to permit c ...
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139 views

Significance of imaginary mass

Can real mass be thought of as producing a deformation in spacetime leading to a stable equilibrium (valley curve in gravitational potential energy) of the massive body, and imaginary mass as similar, ...
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358 views

Misbehaving singular isothermal sphere potential

The singular isothermal sphere (SIS) is a useful simple model often used in astrophysics. It has density profile: $$\rho(r) = \frac{\rho_0 r_0^2}{r^2}$$ This is well known to have some quirks (...
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479 views

Is hydrogen atom in a box solvable analytically?

Schrödinger's equation for hydrogen atom in free space can be easily solved by switching to center of mass frame, introducing reduced mass and separating variables in the resulting 3D problem. But ...
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88 views

Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$ V(x) ~=~0 $$ for $|x| > b $. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...
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Units and missing constants in quintessence expressions?

In cosmology, quintessence is an alternative to the cosmological constant. In this approach (described here), we consider a scalar field $\phi$ and its self-interacting potential $V\left(\phi\right)$ ...
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QM Question about the Dirac Delta Potential

I just wrote down the solution for the bound state of the Dirac delta potential well, for $E<0$, and apparently there is only one specific energy for the bound state, and it is negative. I solved ...
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What is (or where can I discover) the Burke Potential?

I have very much enjoyed William L. Burke's Applied Differential Geometry. Reading around on the web it seems that he discovered something which is called the (retarded) Burke Potential, but I have ...
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108 views

The particle mesh ewald method in two dimensions

I am attempting to implement the particle mesh ewald method (http://dx.doi.org/10.1063/1.470117) in two dimensions. I am wondering what needs to be changed in the method from three dimensions to two ...
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Scattering on delta function potential

Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$. How can one show or explain that $...
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638 views

Infinite quantum well width $L$ to $2L$ adiabatic process

If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
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Resistors equivalent using symmetry and equipotential line

I propose the following statement: In a circuit, while determining equivalent resistance across two points, if the circuit is symmetric wrt the line joining the two points , we may fold the circuit ...
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For degenerate perturbation theory, how do we interpret the eigenvectors and eigenvalues of $\hat V$?

For the eigenvectors that are unmixed by the matrix $\hat V$, the eigenvalues are the energy corrections of this eigenbasis. However, the eigenbasis tends to always be (as far as I'm aware) a linear ...
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Proving continuity of potentials and fields due to a surface charge

Is there a way to show: $(1)\ \displaystyle \phi=\int_{S'} \dfrac{\sigma}{r} dS'$ is continuous all over space $(2)\ \mathbf{E}=\displaystyle\int_{S'} \dfrac{\sigma}{r^2}\ \hat{\mathbf{r}}\ dS'$ is ...
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Doubts about interpretation of the curves of effective potential energy

The image shows a graph of the effective potential energy. Where,$K=-Gm_{1}m_{2}$ and $L$ is the angular momentum. The graph of the effective potential energy that can be seen in this publication was ...
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59 views

electric potential of electric dipole in 2D

I have the homework question as follows. What I did was first find that $$\phi = \frac{-\lambda}{2\pi\epsilon_0}(\ln(r_+)-\ln(r_-))=\frac{-\lambda}{2\pi\epsilon_0}\ln\left(\frac{r_+}{r_-}\right).$$ ...
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77 views

How can theories about 1D or 2D systems be generalized for 3D systems?

I was watching a lecture video from MITx $^\dagger$ by professor Barton Zwiebach. He proved a pretty cool theorem "every attractive 1-dimensional potential has a bound state"; however, that only holds ...
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80 views

1D Time independent Schrodinger eq. with limit

The one dimensional Schrodinger equation for an exponential potential $$-{\hbar^2\over 2m} \frac{d^2\psi}{dx^2}+-\alpha\frac{e^{-\vert x\vert\over\epsilon}}{2\epsilon}\psi=E\psi$$ I am interested ...
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27 views

Relativistic Electric Potetnial

Suppose you have a particle of charge q circling the z axis in the xy plane. The orbit is centered at the origin and has a radius of $r_0$. The angular frequency of the orbit is $\omega$. Position of ...
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23 views

Field between 2 electrodes experiment

We were asked to conduct an experiment that is as follows: Connect 4.5V constant voltage across 2 electrodes of thin Cu wire, dipped in a tub of copper sulfate solution. A needle is connected to a ...
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impossible Poisson's ratio of Lennard-Jones potential type solid (cubic cristal for example), or any potential depending on $r$

We know (for instance : https://en.wikipedia.org/wiki/Poisson%27s_ratio ) that the Poisson ratio is $\nu=1/2-Y/(6B)$, with $Y$ the Young modulus and $B$ the bulk modulus. Let's assume we have a ...
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35 views

What type of potential is suitable for ion bombardment in Molecular Dynamics?

I would like to study ion bombardment on targets with molecular dynamics, especially on oxides. So far I ran conclusive tests with Lennard-Jones potentials, but I would like to obtain better ...
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64 views

Two dimensional hyperbolic potential has no charge density but a surface charge density?

I am learning about electric potential, and I am confused about what exactly is going on in the following situation: Say we have a potential $V =- V_0 \frac{xy}{a^2}$ This means that $\nabla^2V=0$. ...
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29 views

How to calculate the total emf and current in a secondary winding composed of multiple materials

In transformers, flux swings in the primary winding induce an emf in the secondary. Typically the secondary is taken to be a single material, but if it is instead taken to consist of multiple ...
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18 views

Potential profile defined up to a constant

More of a clarification than an actual question. I'm doing exercises on graphing electric fields and the corresponding potential profiles, and i get the same potential profile as my professor, just ...
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77 views

Why use potential functions to solve Maxwell's equations?

I'm reading "Antennas and Wave Propagation" by Harish and Sachidananda. They introduce the phasor form of Maxwell's equations: $$\nabla\times E=-j\omega\mu H$$ $$\nabla\times H = j\omega\epsilon E + ...