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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In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?

A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. Is there a one to one correspondence between the potential and its spectrum? If the answer ...
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Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
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I don't understand what we really mean by voltage drop

This post is my best effort to seek assistance on a topic which is quite vague to me, so that I am struggling to formulate my questions. I hope that someone will be able to figure out what it is I'm ...
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Birds sitting on electric wires: potential difference between the legs

We have seen birds sitting on uninsulated electric wires of high voltage transmission lines overhead without getting harmed, because sitting on only one wire doesn't complete any circuit. But what ...
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What exactly is a bound state and why does it have negative energy?

Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)? Why, when a stable ...
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Why don't we define potential due to a magnetic field?

We define electric potential and gravitational potential and use them quite often to solve problems and explain stuff. But I have never encountered magnetic potential, neither during my study (I am a ...
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What is the difference between electric potential, electrostatic potential, potential difference (PD), voltage and electromotive force (EMF)?

This is a confused part ever since I started learning electricity. What is the difference between electric potential, electrostatic potential, potential difference (PD), voltage and electromotive ...
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Continuity & smoothness of wave function

Is there anything physical that enforces the wave function to be $C^2$? Are weak solutions to the Schrödinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't mention ...
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Why the statement "there exist at least one bound state for negative/attractive potential" doesn't hold for 3D case?

Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal. However, today I'm doing a homework considering a potential like this:$...
an offer can't refuse's user avatar
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4 answers
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Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?

Sorry if this is a silly question but I cant get my head around it.
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22 votes
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Why the electric potential of Earth is zero?

For a localized charge distribution the potential is set to zero far away from the charge distribution (at infinity) Now, when grounding a conductor, i.e. connecting it to Earth, it is said that we ...
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Why do we use potential for quantizing the electromagnetic field?

For quantizing the electromagnetic field authors go to its potential and then find themselves facing to the problems of degree of freedom from gauge transformation. Why we can't simply quantize ...
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How to interpret the magnetic vector potential?

In electromagnetism, we can re-write the electric field in terms of the electric scalar potential, and the magnetic vector potential. That is: $E = -\nabla\phi - \frac{\partial A}{\partial t}$, ...
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Purpose of Using Taylor Series and Multipole Expansion to Approximate Potential

I'm currently taking a third-year electromagnetism course (we use Griffiths), and we have begun covering approximations of our potential function, $\text{V} =\int\frac{k \text{dQ}}{\textbf{||r||}}$, ...
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Why does a Resistor cause a potential drop?

I need to know the underlying physics of what exactly happens different with the electric field in the resistor than in superconducting wires. Why is it that when I connect a resistor, potential drops ...
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In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence?

The Lennard-Jones potential has the form: $$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$$ The (attractive) $r^{-6}$ term describes the ...
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Why are the dineutron and diproton unbound?

It is known that there are no diproton or dineutron nuclei. Does this mean that two protons or neutrons are not actually attracted to each other? Even if the attraction was weak, wouldn't it cause ...
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Hexadecapole potential using point particles?

We can get monopole $1/r$, dipole $1/r^2$, quadrupole $1/r^3$ and octupole $1/r^4$ potential falloff by placing opposite point charges at the corners of a point, line, square and cube, respectively. ...
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6 answers
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Is the harmonic oscillator potential unique in having equally spaced discrete energy levels?

I was wondering if the good old quadratic potential was the only potential with equally spaced eigenvalues. Obviously you can construct others, such as a potential that is infinite in some places and ...
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How is the curl of the electric field possible?

Taking the curl of the electric field must be possible, because Faraday's law involves it: $$\nabla \times \mathbf{E} = - \partial \mathbf{B} / \partial t$$ But I've just looked on Wikipedia, where it ...
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When does the $n$th bound state of a 1D quantum potential have $n$ maxima/minima?

In Moore's introductory physics textbook Six Ideas that Shaped Physics, he describes a set of qualitative rules that first-year physics students can use to sketch energy eigenfunctions in a 1D quantum-...
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3 answers
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What is a gauge in a gauge theory?

As I study Jackson, I am getting really confused with some of its key definitions. Here is what I am getting confused at. When we substituted the electric field and magnetic field in terms of the ...
Roshan Shrestha's user avatar
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1 answer
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3D Delta Potential Well

The 1D delta potential well $V(x) = -A\delta(x - a)$ always has exactly one bound state. The same is true for the 3D delta potential well $V(\vec{r}) = -A\delta(\vec{r}-\vec{a})$. I can show this for $...
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Infinite square well that suddenly decreases in size

A well known exercise in basic quantum mechanics is the sudden (diabatic) increase of the length of an infinite square well. Now consider a particle in an eigenstate of an infinite well that is ...
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When Eigenfunctions/Wavefunctions are real?

When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real? What happens in 1D case like the finite ...
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Would you die if you put your hands on a powerline?

You know how birds perch on powerlines without getting electrocuted? What if by some chance that I find myself falling and I grab on one of them? Let's say both of my hands are on the same line, would ...
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Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
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Shape of water in rotating bucket

I need to show that the surface of water in a bucket rotating with constant angular velocity will have parabolic shape. I'm quite confused by this problem, but here's what I did: $$\vec{F}_{cf} + \...
sequence's user avatar
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What's wrong with Abraham's proposed force law in Nordström's first theory of gravity?

Nordström's 1912 proposed theory of relativistic gravity posited that the gravitational potential field $\phi$ and the matter density field $\rho$ are both scalar fields, simply related by the wave ...
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What maintains constant voltage in a battery?

I know there's lots of questions that address similar situations, (Batteries connected in Parallel, Batteries and fields?, Naive Question About Batteries, and the oft-viewed I don't understand ...
Andres Salas's user avatar
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5 answers
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How can the electric potential be zero at a point where the electric field isn't, if that field can give a test charge kinetic energy?

Say we have 2 charges set up like above. Why is $V_3=0$ ? I can understand mathematically that the scalars fields cancel out, but I don't understand it physically. If I place a positive charge in ...
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Reflectionless potentials in quantum mechanics

Scattering on potential $$V(x) = -\frac{(\hbar a)^2}{m}\text{sech}^2(ax)$$ with 1D equation of Schrodinger is famous problem. It is dealt with in Problem 2.48 of Griffiths book or online here. It is ...
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2 answers
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Degeneracy in one dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a ...
got it--thanks's user avatar
14 votes
4 answers
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Increasing a potential causes increase in energy levels

Suppose a potential $V(x)$, and suppose a bound particle so the allowed energy levels are discrete. Suppose a second potential $\widetilde{V}(x)$ such that $\widetilde{V}(x) \geq V(x)$ for all $x$ (...
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Motivation for Potentials

This is a hypothetical question about "pedagogy". Let's say I am trying to take someone who has just a very small amount of knowledge about Newtonian mechanics and convince them that the Lagrangian ...
Jonathan Gleason's user avatar
13 votes
2 answers
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What is a potential?

I am self-studying electrodynamics and am wanting to know what is meant by a potential. I understand the concept of potential energy but what is meant by a potential? Is it the same thing as a field, ...
Steven's user avatar
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6 answers
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Why is the electric field perpendicular to every point on the surface of a conductor?

I am reading Berkeley Physics Course, Volume 2 (Electricity and Magnetism by Edward M. Purcell). I am in chapter $3$, page $92$, and the book discusses conductors. The following is from the book: ...
Belgi's user avatar
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Stationary states of a triangular prism

I need to find the wavefunctions of the stationary states of a 3d square potential well with its boundaries defined by a triangular prism - like the one illustrated on the wikipedia page: https://en....
Ben's user avatar
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3 answers
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Earthing a conductor

This may be a basic question, but I have never understood it completely: why is an earthed conductor always at zero potential? I would say it is because theoretically one can suck up charge from the ...
user209347's user avatar
12 votes
3 answers
13k views

Pn junction voltage drop?

This image from wikipedia, explains that there occurs a potential drop across a pn semiconductor junction, and an electric field confined to the depletion region. I already know the reason for the ...
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12 votes
5 answers
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Physical meaning of potential in heat equation

I'm working on the mathematical theory of parabolic equations. The prototype of such equations is heat equation given as follows : Let $\Omega$ be a bounded region of the space and $T>0$ a fixed ...
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How does one prove that Energy = Voltage x Charge?

We know $$E = q V$$ where $E$ is the energy (in Joules), $V$ is the potential difference (in Volts), and $q$ is the charge. Why is this equation true and how we prove it?
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1 answer
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Gravity vs. EM: action at a distance

Countless texts point to Newton's theory $\nabla^2\phi = 4\pi G\rho$, and remark that the problem here is that a distribution of mass determines the potential instantaneously everywhere, which is ...
Khun Chang's user avatar
12 votes
2 answers
10k views

How electric currents can flow between 2 points at the same potential?

According to Ohm's law, if there is a potential difference, $V$, across a resistor then there is a current, $I$, flowing through it. Since we assume that points along the connecting wire are at the ...
Revo's user avatar
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Coulomb potential in 2D

I know that the Coulomb potential is logarithmic is two dimensions, and that (see for instance this paper: http://pil.phys.uniroma1.it/~satlongrange/abstracts/samaj.pdf) a length scale naturally ...
zakk's user avatar
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2 answers
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Why do we like gauge potentials so much?

Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about ...
Isaac's user avatar
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1 answer
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Grounding system of conducting plates

So, I always make mistakes on problems such as this (the grounding part), so I'm hoping someone could really explain to me how the process works. There are $n$ large parallel plate conductors ...
Koolman's user avatar
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From Liénard-Wiechert to Feynman potential expression

When studying the potential of an uniformly moving charge in vacuum, Feynman proposes to apply a Lorentz transformation on the Coulomb potential, which reads in the rest frame $ \phi'(\mathbf r',t') =...
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4 answers
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Force as gradient of scalar potential energy

My text book reads If a particle is acted upon by the forces which are conservative; that is, if the forces are derivable from a scalar potential energy function in manner $ F=-\nabla V $. I was ...
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12 votes
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Deriving non-relativistic potentials from QFT

Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
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