The potential tag has no wiki summary.
20
votes
4answers
758 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 ...
14
votes
6answers
950 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 ...
10
votes
1answer
242 views
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 ...
9
votes
2answers
216 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 ...
8
votes
8answers
3k views
What is the difference between electric potential, voltage and electromotive force?
This is a confused part ever since I started learning electricity. What is the difference between voltage and electromotive force (emf)? Both of them have the same SI unit, right? I would appreciate ...
7
votes
1answer
555 views
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 ...
6
votes
2answers
269 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 ...
5
votes
2answers
269 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 ...
5
votes
2answers
129 views
Is there a time delay during tunnelling?
A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process?
5
votes
1answer
108 views
Apparent contradiction between calculations and intuition?
I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with.
We have a potential step ...
4
votes
4answers
2k views
Infinitely charged wire and Differential form of Gauss' Law
I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get
$$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty ...
4
votes
1answer
276 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}$, ...
4
votes
1answer
127 views
Kaluza-Klein Christoffel Symbols
I have a question regarding the connection coefficients as they pertain to the following paper: http://www.weylmann.com/kaluza.pdf . When I try to calculate the 4D Christoffel symbols from the 4D part ...
4
votes
2answers
233 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 ...
4
votes
1answer
112 views
Linear dependence of magnetic potential on current density
I'm a mathematician learning physics to provide some background for my mathematical work (especially pde's!). I have been reading through Jackson's Classical Electrodynamics (3rd edition), and I was ...
4
votes
1answer
121 views
Loopless voltage measurement
I think we are all very well familiarized with the classical voltmeter. Classical voltmeter has two conducting wires that bring two potentials into the box. In the box we have well controlled ...
4
votes
3answers
2k views
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 ...
3
votes
2answers
212 views
Alternative definitions of potential?
I hope this question is simple and can be quickly cleared up.
In a 1D conservative dynamical system, I've always been taught that the potential function is the function $V(x)$ such that:
...
3
votes
2answers
254 views
How can you have a negative voltage?
How can you have a negative voltage? I don't really understand the concept of negative voltage, how can it exist?
3
votes
1answer
138 views
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, ...
3
votes
1answer
552 views
Electric Potential of a Charged Sphere
Problem Consider a sphere with radius $R$, and with a charge distribution $\rho(r)=\rho_0r$. Using Poisson's equation, calculate the electric potential inside and outside the sphere.
Solution I don't ...
3
votes
3answers
356 views
Can we have discontinuous wavefunctions in the Infinite Square well?
The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
3
votes
1answer
299 views
Can we solve the particle in an infinite well in QM using creation and annihilation operators?
The particle in an infinite potential well in QM is usually solved by easily solving Schrodinger differential equation. On the other hand particle in the harmonic oscillator oscillator potential can ...
3
votes
3answers
318 views
About constructing potential energy functions
There are many classical systems with different potential functions. My problem is that I do not understand how one can construct a certain potential function for a certain system. Are there any ...
3
votes
0answers
116 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, ...
2
votes
2answers
286 views
Plotting $\psi$ for finite square well potential
Lets say we have a finite square potential well like below:
This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
2
votes
4answers
718 views
How does instant charging of one plate affect the potential of the other plate of a floating capacitor?
If I have an uncharged floating capacitor and I instantaneously connect one plate to some potential, then that plate will acquire some charge. In practice, the other floating plate will ...
2
votes
3answers
2k views
How does electricity flow in conductor when potential difference is applied?
Electrons move from higher potential to lower potential. When a conductor is connected to battery, electron move from negative terminal to positive terminal.
But the battery itself forms a Electric ...
2
votes
2answers
2k views
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 ...
2
votes
6answers
317 views
Is voltage electric potential or electric potential difference?
On Wikipedia, voltage is defined to be the electric potential difference. However, I am still not certain as to whether voltage is the electric potential ($PE/q$) or electric potential change ...
2
votes
6answers
359 views
Electrostatic Potential Energy Derivation
How is the boxed step , physically as well as mathematically justified and correct ?
Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy
As work done = $- \Delta U $. for Conservative ...
2
votes
2answers
707 views
Electric potential due to a point charge in Gaussian/CGS units
I learned electrostatics in SI units. In SI, the electrostatic potential due to a point charge $q$ located at $\textbf{r}$ is given by
$\Phi(\textbf{r}) = \frac{q}{4 \pi \epsilon_0 |\textbf{r}|}$.
...
2
votes
1answer
498 views
Gradient of the electric potential
I was wondering if for a point-like charged object, does the gradient of the electric potential point in the direction of maximum increase or maximum decrease of the function $V$?
2
votes
2answers
139 views
Differences In Potential Equations
Could someone please describe the differences between the uses each of these potential equations:
Potential due to a point charge:
$V = \frac{k \cdot q}{r} - \frac{k \cdot ...
2
votes
2answers
701 views
What is the potential difference between point X and point Y?
Here is the problem:
In the above figure I want help on finding the potential difference between X and Y.
It is getting quite confusing due to the battery in the middle. I found the current in both ...
2
votes
2answers
137 views
Why does a capacitor discharge?
Suppose a charged capacitor (parallel plates), the negative and positive charges on two plates attract each other. Which force cause the negative charge carriers (electrons) move through the circuit ...
2
votes
2answers
80 views
The appearance of volume $V$ in the Fourier series representation of a periodic cubic system
In the textbook Understanding Molecular Simulation by Frenkel and Smit (Second Edition), the authors represent a function $f(\textbf{r})$ (which depends on the coordinates of a periodic system) as a ...
2
votes
1answer
217 views
Higgs potential
The potential for the Higgs field is standard a quartic one (Mexican hat). Is this done for simplicity or are there fundamental reasons for this choice? I can imagine further contributions to this ...
2
votes
2answers
279 views
Higher To Lower Electric Potential
The question I am working on is:
"An electron moving parallel to the x axis has an initial speed of $4.65 \cdot 10^6~m/s$ at the origin. Its speed is reduced to $1.27 \cdot 10^5 ~m/s$ at the point ...
2
votes
2answers
187 views
Classical limit of a quantum system
If we have a one dimensional system where the potential
$$V~=~\begin{cases}\infty & |x|\geq d, \\ a\delta(x) &|x|<d, \end{cases}$$
where $a,d >0$ are positive constants, what then is ...
2
votes
1answer
809 views
How to solve Schrodinger Equation - Tunnelling
I have to solve analitically the Schrodinger equation in one-dimension with a barrier of potential (tunnel effect):
$$ih \frac{d}{dt} U(x,t) = \left[ \left(-h^2 \frac{d^2}{dx^2} \right) + q V(x) ...
2
votes
3answers
205 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.
2
votes
1answer
767 views
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 ...
2
votes
2answers
561 views
Electric potential of sphere
(a) I am a little confused about this part. The point at A to B isn't radial. The electric field is radially outward, but if I look at the integral
$$\int_{a}^{b}\mathbf{E}\cdot d\mathbf{s} = ...
2
votes
1answer
424 views
How is capacitance defined for three concentric spheres?
If we have a configuration of metal concentric spheres (each of negligible thickness) of radii $r_1,r_2,r_3$ respectively and $r_1<r_2<r_3$, and we are given the potentials of the spheres to be ...
2
votes
1answer
131 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.
2
votes
2answers
361 views
Why do two ends of a long conducting wire have the same electric potential?
I am not seeing the "big picture" here. If I have two conducting spheres separated by a long conducting wire, why would the spheres share the same electric potential?
I think of the spheres as point ...
2
votes
0answers
40 views
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 ...
2
votes
0answers
56 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 ...
1
vote
4answers
299 views
Why does it seem that the potential difference dependence of capacitance and total energy stored in a parallel-plate capacitor are contradictory?
Consider a parallel-plate capacitor. Charge is stored physically on electrodes ("plates") which are flat and parallel to one another. If one electrode has charge $+Q$ and the other electrode has ...
