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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46
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7answers
3k views

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 ...
37
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15answers
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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 ...
33
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4answers
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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 ...
29
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6answers
4k views

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 ...
22
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11answers
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What is the difference between electric 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, potential difference (PD), voltage and electromotive force (EMF)? All of them have ...
19
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5answers
2k views

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 ...
19
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1answer
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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 ...
17
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3answers
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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:$...
17
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6answers
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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 ...
16
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4answers
3k views

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.
15
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4answers
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What exactly is a bound state and why does it have negative energy?

Our professor hasn't explained what bound states are. Could you give me an idea of what they mean and their importance in quantum-mechanics problems with a potential (e.g. a potential described by a ...
15
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1answer
3k views

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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3answers
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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 ...
14
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3answers
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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 ...
14
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2answers
10k views

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, ...
14
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4answers
964 views

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 $x$ (...
14
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3answers
769 views

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 ...
13
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1answer
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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 $...
13
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3answers
1k views

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 ...
13
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1answer
514 views

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....
12
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2answers
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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 ...
12
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2answers
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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. ...
12
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1answer
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When does the $n$th bound state of a 1-D 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 1-D ...
11
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2answers
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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 ...
11
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6answers
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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: ...
11
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5answers
484 views

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 ...
11
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2answers
844 views

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 ...
11
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2answers
9k 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 ...
10
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5answers
33k views

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 ...
10
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1answer
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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 ...
10
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2answers
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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 potential $V(x)...
10
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2answers
878 views

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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2answers
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Triangular barrier in infinite potential well

Suppose I am looking to solve the wavefunction for the following 1D potential: $$U(x) = \begin{cases}V_0\frac{a-|x|}{a}&\quad\text{for}\quad|x|<a \\\infty&\quad\text{for}\quad|x|>a\end{...
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4answers
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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 ...
9
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3answers
3k views

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 ...
9
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5answers
2k views

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 ...
9
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2answers
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Why is the work done on a charge calculated from infinity?

Why is the work done on a charge calculated from infinity to a point? Why not from one particular point to other?
9
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8answers
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Does Ohm's law $V = IR$ mean voltage causes current, or does it just say that voltage and current are related?

I have read that Ohm's law, $V=IR ,$ just means that $V$ is equivalent to $IR ,$ not that voltage is the cause of current. This is similar to the interpretation of Newton's second law, $\mathbf{F} = ...
9
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3answers
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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 ...
9
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6answers
24k views

Why is electric potential scalar?

I can't conceptually visualize why it would be so. Say you have two point charges of equal charge and a point right in the middle of them. The potential of that charge, mathematically, is proportional ...
9
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2answers
212 views

Why are we allowed to divide by $\psi$ when $\psi=0$?

When Griffiths derives the time-independent Schrodinger equation he divides both sides of the Schrodinger equation by $\psi$. I take this as a tacit assumption that $\psi\neq0$ when we intend to solve ...
9
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3answers
834 views

Why do we use gauges in Maxwell equation?

While solving the Maxwell's equation we often use the Lorenz or Coulomb gauge, but why is that? Are the equations unsolvable if the gauge is not fixed? Or is it just for the simplicity?
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2answers
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Infinite and Finite Square Wells

For the infinite square well in the first region, outside the well: $$\frac{-\hbar^2}{2m}\frac{d^2 \psi}{dx^2} + V(x) \psi (x) = E \psi (x),$$ where you set $V = 0$. Rearranging gives $$\frac{d^2 \...
9
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2answers
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Particle in a 1D Box with Symmetric potential: How find solutions?

I am working on a problem in which I shall find the normalised solution to the 1D particle in a box. Solving for the particle in an asymmetric potential is quite straight forward, but I run into ...
9
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3answers
8k views

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 ...
8
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6answers
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Potential Nonsense

How is the voltage along the equipotential line between the two equal-opposite charges ZERO? Two common definitions of voltage between points A and B: (1) The net-work per unit charge against the ...
8
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6answers
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Is electromagnetic vector field a sum of E and B?

I have a hard time to fully understand (classical) electromagnetic field theory with respect to Helmholtz's decomposition. Let me start from Helmholtz's theorem: Any vector field of class $C^{\...
8
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3answers
642 views

Is “The curl of the gradient of any scalar field is identically zero” contradictory to Faraday's Law? [duplicate]

$V$ is a scalar field, then $$\nabla\times \nabla V = 0$$ Faraday's law: $$\nabla \times \mathbf{E} = -\frac{d\mathbf{B}}{dt},\\ \mathbf{E} = -\nabla V\, .$$
8
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2answers
784 views

Solution for inverse square potential in $d=3$ spatial dimensions in quantum mechanics [duplicate]

Can a particle in an inverse square potential $$V(r)=-1/r^{2}$$ in $d=3$ spatial dimensions be solved exactly? Also please explain me the physical significance of this potential in comparison with ...
8
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3answers
10k 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 ...