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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347 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?
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3answers
1k 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 ...
1
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0answers
650 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
224 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
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2answers
285 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
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2answers
1k 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} = ...
1
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2answers
281 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 ...
1
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4answers
176 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 ...
1
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2answers
543 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
2k 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 ...
-4
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1answer
1k views

Lennard-Jones potential - equilibrium [closed]

If I have Lennard-Jones potential, how can I calculate equilibrium? $$ U(r)=\epsilon \left ( \left (\frac{r_m}{r} \right )^{12}-2 \left (\frac{r_m}{r}\right )^6 \right ) \ $$
1
vote
1answer
413 views

Why has the Higgs potential the form it has?

The potential for the Higgs field is 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 potential ...
4
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2answers
10k 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 ...
1
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1answer
686 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 ...
2
votes
3answers
11k views

How can I theoretically describe the potential between two capacitors in series?

Suppose to have two capacitors in series: The voltage in the middle point will be: $$ V_X = V_1 \frac{C_1}{C_1+C_2} $$ How can this be explained? It's been asked in electronics, and explained in ...
5
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1answer
128 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 ...
1
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2answers
293 views

Fundamentality of voltage to current

From Ohm's Law : Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. I would like to know if ...
3
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3answers
27k 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 ...
0
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1answer
396 views

Equipotential Contour mapping and making it 3D [closed]

I have seen Contour diagrams for Equipotentials . That are drawn like so: I also saw One image for these contours that was in 3D (Negative Point Charge) : I was Wondering If there's any ...
0
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1answer
885 views

Potential difference between conductors

Reading some books there is something that i don't understand. Is the capacitors topics when they name a potential difference between conductors. As i know, Potential difference is the difference in ...
2
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2answers
2k 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
2answers
293 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 ...
1
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0answers
132 views

An electron is subjected to an electromagnetic field using the canonical equations solve

So I was given the following vector field: $\vec{A}(t)=\{A_{0x}cos(\omega t + \phi_x), A_{0y}cos(\omega t + \phi_y), A_{0z}cos(\omega t + \phi_z)\}$ Where the amplitudes $A_{0i}$ and phase shifts ...
4
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4answers
6k 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 ...
10
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1answer
2k 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 ...
4
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1answer
143 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 ...
8
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2answers
519 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 ...
2
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2answers
107 views

Origin of field deduced from potential

Related: Tubelights+power lines pictures? I would've edited this into the above question, but I realized that there' enough to it to qualify as a new one. Plus this seems to be a confusion of ...
1
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1answer
104 views

Formula for potential for 2 coaxial tubes

Could someone remind me of the formula for potential function for a system consisting of 2 coaxial tubes maintained at a fixed potential difference and the in between medium has uniform conductivity ...
0
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1answer
279 views

Tubelights+power lines pictures?

I've come across many pictures like these, sometimes in chain emails reporting the dangers of power lines. Another claim is that they run on "wasted" energy. The explanations given are that the ...
1
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1answer
2k views

How to calculate the charge and the potential across a charged capacitor charging an uncharged capacitor?

Initially, there is a single capacitor $A$ attached to a power source that charges it to a certain voltage $V$. Once it is charged, it is instantaneously removed and placed in a circuit with an ...
2
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1answer
2k 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(-\hbar^2 \frac{d^2}{dx^2} \right) + q V(x) ...
0
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2answers
1k views

The energy of electric interaction between these dipoles? [closed]

I'm a physics tutor. This is not a homework problem. I'm unable to solve this problem. The energy of electric interaction between these dipoles will be: Choose the correct answer from: I tried ...
4
votes
1answer
493 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 ...
1
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2answers
836 views

Image charges, laplace equation and uniqueness theorem

Consider a well-known problem of the electric field generated by a system composed of a point charge in proximity of a large earthed conductor. It is said that the potential due to an image charge ...
6
votes
4answers
956 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
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2answers
2k 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 ...
1
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1answer
72 views

Potential at a point

What is the electric dipole moment of the charge distribution with $q$ at $(0,0,1)$, $q$ at $(0,0,-1)$ and $-2q$ at $(0,0,0)$? I would think that it is $\vec{0}$ by the definition ...
-1
votes
2answers
209 views

Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]

A particle of mass m moves on the x-axis under the influence of the potential $$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$ Can anyone help me, using Schrödinger's equation in one dimension that the energy ...
2
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2answers
194 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
4answers
2k 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 ...
3
votes
0answers
267 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
1answer
338 views

Complex Potentials, Potentials and Fields

Suppose an electric field $E=-\nabla \psi$ where $\psi=-Q\ln r$ where $Q$ is just some constant and I have found its harmonic conjugate to be $-Q\theta+c$ where $c$ is some constant. What does it say ...
0
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2answers
1k views

How to calculate the electric field at a point in space

Let's say I have a uniformly-charged wire bent into a semi-circle around the origin. How can I find the electric field (magnitude and direction) I'm not even sure if I should use Coulomb's or Gauss' ...
3
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3answers
576 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 ...
2
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1answer
305 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
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1answer
2k 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 ...
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1answer
360 views

A quantum particle in a box (with a catch)

I am reading Shankar's Quantum Mechanics and I am looking at the case where there is one particle inside a box, where the potential is zero inside the wall and abruptly goes to infinity outside the ...
2
votes
7answers
745 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 ...
1
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1answer
6k views

Current against the inverse of resistance graph, $I = V/R +c$

If I have a plot of current ($y$ axis) against 1/Resistance ($x$ axis). The circuit it is measured from is a simply 2 resistors connected in parallel to battery, where the potential across the ...