# 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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### 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 ...
3answers
8k views

### 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 ...
1answer
2k views

### Method of image charges — Why is a *grounded* plate needed?

In the classic image charge problem of a charge $q$ above an infinite grounded plane, it is well known that the field lines essentially behave as though there were a negative charge behind it, and the ...
3answers
4k views

### What is the equation of the gravitational potential in general relativity?

How is the gravitational potential replaced by the metric tensor in general relativity? $$U_G=\frac {GMm}{r}$$ What is its equation?
4answers
5k views

### What is the physical meaning of electric potential, potential difference, and voltage?

When resembling the electricity flow through a wire to people walking through a street: electrons are people, current is the number of people, resistance is the barriers on the way. But what is the ...
2answers
298 views

### Can two different Schrödinger equations have the same wavefunction?

Is it possible for two Schrödinger equations describing different systems to have the same wavefunction? And if that is the case, why or why not?
1answer
997 views

### Concrete example of the application of complex analysis in electrostatics [closed]

I've heard complex analysis can be useful in solving electrostatics problems, but despite doing some research I was unable to find any concrete examples. Would anyone be able to provide a simple ...
2answers
335 views

### Curvature of electrostatic potential is zero

Could you please expound upon this claim? I found such claim on Zangwill's Classical Electrodynamics, which states that constraint coming from Laplacian equation implies electrostatic potential has ...
1answer
400 views

### How do aspherical gravitational monopoles look like?

I was recently pointed by laboussoleestmonpays to a beautiful paper from some time ago, Aspherical gravitational monopoles. Alain Connes, Thibault Damour and Pierre Fayet. Nucl. Phys. B 490 no. 1-2 ...
1answer
686 views

### Why electron can not be found at some node locations in the infinite potential well? [duplicate]

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is $$P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ ...
3answers
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1answer
195 views

### Locally every force admits a potential?

I have a little doubt about a force being or not conservative. Well, as I understood, some forces cannot be expressed as exterior derivative of some scalar potential because the work done by the force ...
2answers
1k views

### A simple demonstration that the electrostatic potential has no extrema in free space

The electrostatic potential $V$ cannot attain a local maximum or minimum in free space (a region of space where there are no charges). The claim makes sense intuitively: if $V$ had a local maximum ...
1answer
703 views

### Resistance and potential difference across it

I have this question that has baffled me for hours now. My question is what really happens when charge passes from one point to another in a circuit for eg what happens when it passes over a resistor....
2answers
359 views

### Why does a electric Potential have to be real, but not a Potential in quantum mechanics?

So I had this Problem when I had to learn about classical electromagnetism: Why is it, that we use complex numbers when calculating stuff, but in the end only the real part is important (for example ...
2answers
1k views

### Bound states for sech-squared potential

I'm working on an introductory qm project, hope somebody has the time to help me (despite the length of this post), it will be highly appreciated. My goal is to determine the bound states and their ...