# 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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### 1D Infinite Square Box Discrete Energy levels but Continous Momenta?

In the 1d particle in the box the energy of the particle should be completely determined by the momentum of the particle that you observe correct? So how can you have discrete energy levels and a ...
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### Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be $\rho(r,\theta,\phi)=e^{-r}$)...
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### Finite, square, potential well

Lets say we have a finite square well symetric around $y$ axis (picture below). I know how and why general solutions to the second order ODE (stationary Schrödinger equation) are as follows for the ...
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### Why doesn't the Standard Model have a whole Potential Zoo?

Is there any strong argument which stops us from including potential terms (may be polynomial or not) for other standard model fields besides the Higgs potential? In other words, why isn't there a ...
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### How can current remain in a super-conducting loop without any applied emf?

Okay, let's say we have a circular wire loop in which there are no positive nuclei for the electrons to collide to. There are only electrons, no force between electrons, neither can they colide with ...
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### Two conducting spheres connected by a wire

There are two conducting spheres of different charge and a conducting wire. After they are connected by the wire, charge flows between the spheres. The charge distributes itself so that the spheres ...
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### What is an “Interaction Hamiltonian”

I'm an undergraduate reading up on some quantum physics so that I can help out more in the lab that I'm working in this summer. In the book I'm reading (Shankar's "Principles of Quantum Mechanics") I ...
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### In $\textbf{f} = -\boldsymbol{\nabla} u$, what is $u$?

I know that force is the negative gradient of the potential: $$\textbf{f} = -\boldsymbol{\nabla} u$$ where force $\textbf{f}$ is a vector and $u$ is a scalar. This is a relatively soft question, ...
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### Velocity-Dependent Potential and Helmholtz Identities

I'm currently working through the book Heisenberg's Quantum Mechanics (Razavy, 2010), and am reading the chapter on classical mechanics. I'm interested in part of their derivative of a generalized ...
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### Why do we assume simply connected domains and continuously differentiable fields in electromagnetism theory?

In many textbooks, including Griffiths', they erroneously claim that a field is irrotational if and only if it is conservative (there exists a scalar potential). This is true only if the domain of ...
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### General solution of Poisson's equation [closed]

How to find general solution of Poisson's equation in electrostatics. $$\nabla^2V=-\frac{\rho}{\epsilon_0}$$ Where, V = electric potential ρ = charge density around any point εₒ = absolute ...
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### Physical meaning of gauge choice in electromagnetism

In electromagnetism, it is often referred to gauges of the electromagnetic field, such as the radiation or Coulomb gauge. As far as I know, the definition of a gauge helps us to redefine the problem ...
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### Intuitive explanation of difference in $r$-dependence between dipole and monopole

For an electric monopole, its potential scales with $\frac{1}{r}$, where $r$ is the distance from the point of interest to the charge. However, for a dipole, its potential scales with $\frac{1}{r^2}$. ...
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### Solving quantum radial equation for infinite potential spherical annulus for $l=0$

There is a mass $m$ in a potential such that $$V(r) = \left\{ \begin{array}{lr} 0, & a \leq r \leq b\\ \infty, & \text{everywhere else} \end{array} \right.$$ ...
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### Potential Difference Between Capacitors in Series

I am struggling to find an answer to this, hopefully relatively simple, question. I had a search on stackexchange but couldn't find anything helpful. We are learning about capacitors in Physics and I ...
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### How to calculate time evolution of a wave function in an 1D infinite square well potential?

A particle in an infinite square well has an initial wavefunction $$\psi (x,0) ~=~ Ax(a-x) \qquad \mathrm{for}\qquad 0\leq x\leq a.$$ Now the question is to calculate $\psi (x,t)$. I have ...
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### Current in a fluorescent tube that is not in a circuit

In Walter Lewin's 8.02 Electricity and Magnetism course, he places a fluorescent tube pointing radially outwards from a large Van de Graaff (VDG) generator. Due to the VDG's E-field, this causes a ...
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### Predicting the value of $n$ for the energy of a wavefunction in the infinite square well by inspection
$$E=\frac{n^2 \pi ^2 \hbar^2}{2ma^2}$$ Is it always possible to tell the value of $n$ by inspecting the shape of the wavefunction in the infinite square well no matter what the value of $a$ is? ...