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1answer
674 views

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 ...
3
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2answers
334 views

Lorenz gauge fixing

Is it always possible to define function $\psi$ satisfying the Lorenz gauge equation $$ \partial_{\mu}\partial^{\mu} \psi + \partial_{\mu}A^{\mu} = 0? $$
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1answer
360 views

Non conducting charged planes

I have two parallel non conducting charged planes with opposite charges $6\mu C/m^2$, area $A = 3m^2$ and distance between the planes $d = 0.004 m$. I know the potential between these two planes is ...
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1answer
76 views

Electric charge and the distance

The strength of an electric field is: $E = 200\ \mathrm{N/C}$ The potential (of the test charge) is: $V = 600\ \mathrm{V}$ $\epsilon_r=1$ I need to calculate the distance between this point and the ...
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3answers
672 views

Potential Inside Conducting Cube

A cubical box with sides of length L consists of six metal plates. Five sides of the box { the plates at $x=0, x=L, y=0, y=L, z=0$ - are grounded. The top of the box (at z = L) is made of a separate ...
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1answer
2k views

Electron volt and Voltage

Voltage is the work done per unit charge. Given by: V = W/q Electron volt is the maximum kinetic energy gained by the electron in falling through a potential difference of 1 volt. Given by: K.E ...
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1answer
190 views

Spring Constant

Is it possible to determine the spring constant of a spring in a situation in which it is being compressed when such certain length of compression is not known? If so, how can such calculation be ...
0
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1answer
72 views

how quantum-mechanical particles react in the potential?

I am reading some materials on quantum mechanics. I am a bit confusing in the chapter on wave-particle duality and following questions arise In classical mechanics, the force a particle experience is ...
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1answer
2k 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 $V$?
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2answers
470 views

Wavefunction restrictions of odd potentials

So I was just reading back through Griffiths' "Introduction to Quantum Mechanics" and solving some of the problems for practice. There is a nice one (problem 2.1c for those playing at home) where you ...
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1answer
95 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 ...
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6answers
2k 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 ...
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4answers
4k 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 ...
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2answers
2k 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 ...
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votes
1answer
210 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 ...
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1answer
1k 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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2answers
2k views

Particle in infinite potential well which is doubled in size at $t_0$

I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding. The Problem: A Particle sits in an infinite potential well ...
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1answer
459 views

Electric field of a flat metal plate and a point particle

I'm currently studying electric potential, and I'm having trouble with one of the problems on my homework: A) A point particle with charge $+q$ is on the x-axis at a distance $d$ from the origin, ...
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2answers
248 views

How can one determine at which distance the Lennard-Jones potential reaches a given value?

My question is fairly simple, but I do need clarification on how to get the inverse of the Lennard-Jones potential V(x). I am working with the following expression: $$ V(x) = e\times[(R/x)^{12} ...
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2answers
567 views

Vector Potential and Gauge Invariance in Quantum Mechanics

In classical electromagnetism, we are allowed to use gauge invariance through the argument that the only physical observable fields are the $E$-field and the $B$-field. So in that sense the scalar ...
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1answer
147 views

Is it possible to charge a capacitor to any potential? Does it depend on the dielectric placed between them?

Is it possible to charge a capacitor to any potential? Does it depend on the dielectric placed between them? Or, are there other factors affecting it?
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2answers
5k 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?
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1answer
736 views

( Legendre Generating Function) Off axis Electric Potential from an insulated disk

An insulated disk, uniform surface charge density $\sigma$, of radius $R$ is laid on the $x,y$ plane. Deduce the electric potential $V(z)$ along the z-axis. Next consider an off axis point $p'$, ...
4
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1answer
226 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 ...
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2answers
190 views

Elastic potential

I have a doubt: elastic potential energy is given by: $U=\frac{k}{2}x^2+K$ but does elastic potential exist? (for example: potential gravitational energy is given by $U=mgz+K$ and gravitational ...
1
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1answer
367 views

Does a particle in a spherically symmetric infinite square well potential exert a force on the inner and outer shell barrier?

For a particle in the potential: $$V(r) = \begin{cases} 0 & \text{a < r < b}\\ \infty & \text{otherwise.} \end{cases}$$ Does this guy in the ground-state exert a force on the shells a ...
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2answers
819 views

Highest man-made voltage

What was the highest voltage achieved and was it produced by electrostatic means or just some transformers and multipliers? What are the limitations when it comes to producing voltage using ...
0
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1answer
212 views

About voltage and charge of van de graff generator

I have read that in case of Van de graff generator $V=kQ/r$ where $r$ is radius of the sphere. If that's the case, does the same voltage results in bigger charges in bigger radii?
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1answer
2k views

Maxwell's Correction to Ampere's Law

I have not yet officially studied Electromagnetism but am trying to teach myself at the moment. I understand Maxwell's equations in the context of Magneto- and Electrostatics: they are equivalent, ...
3
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1answer
1k 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 ...
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2answers
1k 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 ...
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0answers
52 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 ...
1
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1answer
993 views

Schrödinger function: Separable wave function with even potential function of x

I have done the Problem 2.1 in Griffiths' quantum mechanics, and it seems not making sense to me. What if the wave function isn't symmetric at all? Then obviously the proof doesn't work. The ...
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2answers
860 views

Find the quantity of charge - given potential function

A potential function is given by $V(r)=\frac{Ae^{-\lambda r}}{r}$ Find charge density and hence charge. I first took the gradient of potential to get $\vec{E}(r)=\frac{Ae^{-\lambda ...
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1answer
595 views

Force exerted on potential wall

A particle bound in an infinite potential wall at $x=0$ will apply a force on the wall. For a plane wave and imagining it as a fluid bouncing off the reflection wall at $x=0$, find the force in terms ...
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1answer
45 views

growth condition for the potential

what growth conditions should the potential inside the Hamiltonian $ H=p^{2}+ V(x) $ has in order to get ALWAYS a discrete spectrum ?? for example how can we know for teh cases $ |x|^{a} $ , $ ...
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5answers
10k views

Electric potential vs potential difference

What is the difference between electric potential and potential difference? In our course book, they are given as separate topics but their definition is given the same.
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0answers
77 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 ...
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2answers
2k views

Barrier in an infinite double well

I am stuck on a QM homework problem. The setup is this: (To be clear, the potential in the left and rightmost regions is $0$ while the potential in the center region is $V_0$, and the wavefunction ...
0
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1answer
92 views

a positive potential as $ x \rightarrow \infty $

let us suppose i can calculate the asymptotic of any potential $ V(x) $ in one dimension , and that i manage to prove that $ V(x) \ge 0 $ as $ x \rightarrow \infty $ could i conclude taht if or big ...
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2answers
263 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?
3
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3answers
756 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 ...
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0answers
516 views

Scattering on delta function potential

Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$. How can one show or explain that ...
3
votes
1answer
185 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, ...
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2answers
187 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 ...
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2answers
875 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} = ...
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2answers
256 views

What does $\textbf{f} = -\boldsymbol{\nabla} u$ mean in practice and how is it computed?

In classical computer simulations such as molecular dynamics (MD) simulations, one integrates Newton's equations of motion to determine particle trajectories. If we think of Newton's Second Law as ...
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4answers
163 views

The notion of bounded states in quantum mechanics and their characterization with operators

Is there any case of potential $V$, such that the continuity of the operator $H=c\ \Delta+V$ is not spoiled? And I don't know any non-differnetial operator examples for continous spectra. I ...
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2answers
406 views

Does the potential energy related to a particle determines its rest mass?

Would it be possible to determine the rest mass of a particle by computing the potential energy related to the presence (existence) of the particle, if this potential energy could be determined ...
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4answers
1k 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 ...