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.

324 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
7
votes
2answers
1k 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 ...
6
votes
0answers
200 views

Sphere half-submerged on a dielectric

This is a classic problem in electrostatics with a twist, so I thought it could be useful for others here. I did have a problem with the integration at the end, but on general I think the idea can ...
5
votes
0answers
164 views

$D$-dimensional Schrodinger's equation with a Dirac delta potential

I know that for $D\geq 2$, there is no bound state for a Dirac potential $V=-\alpha \delta(\textbf{x})$ unless we use an ultraviolet cutoff $k_{max}=1/a$. I showed this by solving the Schrodinger's ...
4
votes
0answers
18 views

Why is the spin-orbit interaction for a nucleus so much more important than the spin-orbit interaction in atomic physics?

In atomic physics, the spin-orbit is a small correction between 1/1000 and 10ppm, so fairly small. In contrast, in nuclear physics the inclusion of the spin-orbit interaction is necessary to reproduce ...
4
votes
0answers
229 views

Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
3
votes
2answers
48 views

Common potential in Capacitors

If two isolated charged capacitors (of different capacitance) are connected in parallel to each other they acquire a common potential. But suppose if i connect positive plate of one capacitor to ...
3
votes
0answers
63 views

Maxwell theory : How to justify the potential gauge fields if there are magnetic monopoles?

Without magnetic monopoles, the Maxwell equations are these (I'm dropping vector notations and all constants, for simplicity): \begin{align} \nabla \cdot E &= \rho_{elec}, \tag{1} \\[12pt] \nabla \...
3
votes
0answers
117 views

What is a good analogy for electric potential?

When the electrical field was defined I could totally relate to $\vec{E}$ being like $\vec{g}$ in mechanics. But for the electric potential I don't know what would be equivalent analogy. Any ...
3
votes
0answers
101 views

How to derive the simplest 1D Superpotential Hamiltonian?

In the superpotential wiki article there are definitions of two supersymmetric operators: $$Q_1=\frac{1}{2}\left[(p-iW)b+(p+iW)b^\dagger\right] \\ Q_2=\frac{i}{2}\left[(p-iW)b-(p+iW)b^\dagger\right] $$...
3
votes
3answers
1k views

Method of image charges for a point charge and a non-grounded conducting plane

I know how to solve Laplace's equation for a point charge in front of a grounded conducting infinite plane. But I want to know what happens (both physics and math) when the infinite conducting plane ...
3
votes
1answer
104 views

Is there something wrong in my book's derivation of work done on charge?

For finding potential at a point due to a +ve charge $(q)$, we find work done to move a unit +ve charge $(q_o)$ from infinity to that point in the presence of +ve charge $(q)$ Since both charges ...
3
votes
0answers
309 views

Accelerated ion beam current

If an electron gun creates a $10\space mA$ electron beam and each electron collides with a gas atom and creates an ion through impact ionization, can the ions then be accelerated with a separate ...
3
votes
0answers
101 views

Conservation of momentum in statistical physics in presence of a potential

Imagine a number of particles, all confined in a parabolic potential. The particles initially have a random velocity and are let free to bounce off each other (say, it's rigid spheres). Does ...
3
votes
1answer
201 views

Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
3
votes
1answer
61 views

Meaning of potential in a discharging capacitor

I am dealing with this thing I cannot figure out. When a capacitor is discharging, the electric field inside it varies with time so we cannot perform the line integral to determine the potential ...
3
votes
0answers
123 views

Is the “Force” of Gravity Simply Hamilton's Principle on a Curved Spacetime?

It's my understanding that General Relativity abstracts away the concept of gravity as a force, and instead describes it as a feature of spacetime by which massive objects cause curvature. Then it ...
3
votes
0answers
85 views

Charge distribution and potential in a 1-dimensional quasistatic system

Suppose you have an 1-dimensional system with a charge distribution $\rho(x)$ (not given) moving with an speed $v(x)$ (not given), calculate the potential $\phi(x)$ and the charge distribution $\rho(...
3
votes
0answers
408 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, ...
3
votes
1answer
86 views

Power series solution for a shifted spherical harmonic oscillator

I'm trying to solve the Schrodinger equation for a radial Harmonic oscillator whos equilibrium point has been shifted away from the origin, i.e. $V(r) = V_0(r-1)^2$. The standard approach is to make ...
2
votes
0answers
39 views

What exactly do the zero-modes of the instanton mean?

I am studying instantons in quantum mechanics. My question is regarding the the zero mode of the fluctuation determinant that we get because the solution for the instanton breaks time translation ...
2
votes
1answer
39 views

Gravitational Potential Derivation

The definition of Gravitational Potential at a point is the work done per unit mass in moving it from infinity to that point. However the work is positive and if you perform the integral you get a ...
2
votes
1answer
40 views

Effective potential in a time-dependent spacetime

My question is regarding an arbitrary time-dependent spherically symmetric spacetime with line-element, in co-moving coordinates, to be $$ds^2 = -f(R) dt^2 + a(t)\bigg\lbrace\frac{dR^2}{f(R)} +R^2d\...
2
votes
2answers
39 views

Is the voltage between the two points $A$ and $B$ denoted as $U_{AB}$ or $U_{BA}$? And why?

Consider the following circuit Is the voltage between the two points $A$ and $B$ denoted as $U_{AB}$ or $U_{BA}$? And why?
2
votes
0answers
27 views

Would the voltmeters give different readings in a circuit with induced current?

$\def\vE{{\vec{E}}}$ $\def\vD{{\vec{D}}}$ $\def\vB{{\vec{B}}}$ $\def\vJ{{\vec{J}}}$ $\def\vr{{\vec{r}}}$ $\def\vA{{\vec{A}}}$ $\def\vH{{\vec{H}}}$ $\def\ddt{\frac{d}{dt}}$ $\def\rot{\operatorname{rot}}...
2
votes
1answer
48 views

Difference, in terms of completeness, between the Dirac well and barrier

I was in my undergraduate QM lecture and we just finished with the Dirac barrier. My question is as follows: We know that the Dirac well’s complete set of solutions requires one bound state and an ...
2
votes
0answers
86 views

What does it mean for a potential not to have a Fourier transform?

Consider an isotropic potential $\phi(r)$ corresponding to the classical force of interaction between two point-particles. The Fourier transform of this potential $$ \Phi(k) = \int \exp(-i\vec k\cdot\...
2
votes
0answers
81 views

Multipole expansions: test on a function $\zeta=\zeta(t)$

Considering the potential $\psi(r)$ of a sphere of mass $M$ with density $\rho(\mathbf r')$, connected by a small volume positioned in the $P'$ point as shown in the figure: The $\psi(r)$ is: $$\...
2
votes
0answers
95 views

Which test function (under variational method of approximation) should be used for a linear potential?

There is this problem, it is not for evaluation, I mean, it is not homework. There is a 3-dimension potential $V(r)=C . r$, where $r$ is the radial coordinate and $C$ is a real constant (I think it ...
2
votes
0answers
62 views

Vector potential of a partially-known magnetic field

let's consider a three-dimensional space permeated by a known magnetic field $\vec{B}$. Let's consider in this space a topologically spherical surface $\mathcal{S}$ centred in the origin. I put a ...
2
votes
0answers
51 views

The formula for the average number of fermions $\langle N \rangle$

In the context of Fermi gases (or fluids in general), one would typically in the grand-canonical formalism use the formula $\langle N \rangle = -\frac{\partial \psi}{\partial \mu}$, where $\psi$ is ...
2
votes
1answer
106 views

Numerical solutions for time-dependent Hamiltonian

Currently I am facing the problem to solve numerically the following equation for a double well harmonic potential: $$i\hbar \frac{\partial}{\partial t}\psi(x,t)= -\frac{\hbar}{2m}\frac{\partial^2}{\...
2
votes
1answer
91 views

Does the potential $V(φ)$ of a scalar field decrease with the expansion of space?

If a scalar field (eg. inflaton field) starts with a high potential. Does the potential $V(φ)$ of the scalar field decrease with the expansion of space? If it doesn’t decrease, would it mean that ...
2
votes
0answers
180 views

Standing spherical wave solution

Let's say we have a spherically symmetric light wave $u(r,t,\theta,\phi)= u(r,t)$ that satisfies the following wave equation with spherically symmetric potential $V(r)=2/r^2$ (also set $c= 1$ so $\...
2
votes
1answer
108 views

Why can't I add the energies in this WKB approximation example to get the allowed energies for the given potential?

Use the WKB approximation to find the allowed energies ($E_n$) of an infinite square well with a "shelf", of height $V_0$ extending half-way across: $$V(x)=V_0 \quad , \text{if} \quad 0<x<a/...
2
votes
1answer
80 views

Do 2 conductors (1 grounded via resistor) reach equipotential, before surplus electrons drain to earth?

Case I: a negative conductor makes contact with a neutral conductor. Negative donates some electrons to neutral, until there is 0 potential difference. Then they both are slightly negative. This ...
2
votes
0answers
69 views

What if in potentiometer, the loops are not balanced to cancel the potential and current flows?

As described in the book (image) that loops should be balanced with equal potential with help of the galvanometer. What if the we do not balance it to zero and have some current flowing? Can we still ...
2
votes
0answers
182 views

Derivation of Feynman Rules for a $\frac{1}{\phi}$ potential

The question is more mathematical in nature. If one had a potential $V(\phi) = \frac{\lambda}{\phi}$, where $\lambda$ is a constant, then how does one derive the Feynman rules for this scalar field's ...
2
votes
0answers
438 views

Dirac Delta potential and perturbation

I have a Dirac Delta potential as follows : $$V(x)= - \alpha \delta (x)$$ I know how to solve that problem. There is exactly one bound state. Now let's say I have an initial wave function in this ...
2
votes
0answers
903 views

Solving the Poisson equation using Green's function

Edit: should I perhaps post this question at math.stackexchange? It seems to me that physics maybe isn't really the right place for it, as it is more about mathematical methods. I have the following ...
2
votes
0answers
477 views

Guess the wave function in a given potential

Are there any techniques in guessing the ground state wave function in any given potential? For example, for a given potential like $$ \frac{1}{1-x^2}$$ or $$ \frac{1}{1-x^3}~?$$ I know wave ...
2
votes
0answers
42 views

Gauge Permitting c Magnetic Vector and Instant Electric Scalar Potentials?

The Lorenz gauge requires c propagation of both scalar and vector potentials. The Coulomb gauge requires instant "propagation" of these potentials but is stated in such a way as to permit c ...
2
votes
0answers
148 views

Significance of imaginary mass

Can real mass be thought of as producing a deformation in spacetime leading to a stable equilibrium (valley curve in gravitational potential energy) of the massive body, and imaginary mass as similar, ...
2
votes
0answers
373 views

Misbehaving singular isothermal sphere potential

The singular isothermal sphere (SIS) is a useful simple model often used in astrophysics. It has density profile: $$\rho(r) = \frac{\rho_0 r_0^2}{r^2}$$ This is well known to have some quirks (...
2
votes
1answer
95 views

Is it possible for two polarizable bodies to induce dipoles in each other in the absence of an external electric field?

If there exist two initially neutral bodies (say atoms) some distance apart, with no external electric field applied, can they induce dipoles within each other?
2
votes
0answers
490 views

Is hydrogen atom in a box solvable analytically?

Schrödinger's equation for hydrogen atom in free space can be easily solved by switching to center of mass frame, introducing reduced mass and separating variables in the resulting 3D problem. But ...
2
votes
1answer
92 views

Is there a mathematical explanation for why there occur bound states if the effective potential falls below zero?

Usually in physics textbooks, if the effective potential of the radial schroedinger equation $$-\frac{d^2}{dr^2}u(r) + \frac{\ell(\ell+1)}{r^2}u(r) + V(r)u(r) = E u(r)$$ falls below zero in some ...
2
votes
0answers
89 views

Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$ V(x) ~=~0 $$ for $|x| > b $. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...
2
votes
0answers
267 views

General potential of rotating system

I'm new here at the physics site, and not really that deep into the area of which i'm going to ask a question about now. Therefore please feel free to ask clarifying questions. I'm trying to deal ...
2
votes
0answers
78 views

Units and missing constants in quintessence expressions?

In cosmology, quintessence is an alternative to the cosmological constant. In this approach (described here), we consider a scalar field $\phi$ and its self-interacting potential $V\left(\phi\right)$ ...
2
votes
0answers
640 views

QM Question about the Dirac Delta Potential

I just wrote down the solution for the bound state of the Dirac delta potential well, for $E<0$, and apparently there is only one specific energy for the bound state, and it is negative. I solved ...