Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the potential-energy tag.

learn more… | top users | synonyms

0
votes
0answers
7 views

Constructing a dc circuit with different input and output currents and voltages? [migrated]

I am trying to answer this question (at the moment I am looking at part a) only as I still have not figured it out): But what I do not understand is how you can change the input and output of dc? I ...
1
vote
0answers
75 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 ...
0
votes
0answers
24 views

How to compute minimum shallowness of quantum well to have at least one bound state?

Given a potential $V$, how does one compute how shallow the potential can be such that it allows at least one bound state?
2
votes
1answer
41 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 ...
1
vote
5answers
118 views

Physical interpretation of the statement $\oint E\cdot dl=0$

Can anyone provide me with a physical interpretation of $\oint E\cdot d\ell=0$ in electrostatics?
3
votes
1answer
47 views

Estimate for minimum potential depth required for bound states in 3D attractive potential well

Consider a 3D spherically symmetric potential well, $$H = \frac{p^2}{2m} + V(r)$$ with $V(r) = - V_0$ for $r < a/2$ and $0$ else, for some $V_0 > 0$. Now, it is well known that $V_0$ needs to ...
3
votes
1answer
67 views

Maxwell's Equations, cast in terms of magnetic vector potential [closed]

Derive $$ \nabla \times \frac{1}{\mu_r} \nabla \times A + \mu_0 \sigma \frac{\partial A}{\partial t} + \mu_0 \frac{\partial}{\partial t} \left( \epsilon_0 \epsilon_r \frac{\partial A}{\partial t} - ...
1
vote
1answer
62 views

Realistic Potential Wells

What is meant by the term "realistic" potential wells? I got stuck into the term as I don't know what are the limitations of the word realistic in this case. For example mentioned in line We ...
3
votes
1answer
25 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 ...
0
votes
1answer
21 views

Can you derive reaction rates from the potential difference across a battery?

There were several cases where I was able to (relatively easily) derive potentials for interactions in my statistical mechanics course. I know that there is no real way to derive the kinetics of a ...
1
vote
1answer
41 views

Current in a fluorescent tube that is not in a circuit

In Walter Lewin's 8.02 Electricity and Magnetism course, he places a fluorescent tube pointing radially outwards from a large Van der Graaf (VDG) generator. Due to the VDG's E-field, this causes a ...
2
votes
3answers
77 views

General question about the potential barrier problem: Why does $\exp( kx)$ diverge when $x>0$ in the case when $E < V(x)$?

For the two images below, the first potential barrier has particles approaching it where $E > V_o$ & the second has a particle that has $E < V_o$, where $E$ is the energy of the particles ...
0
votes
2answers
49 views

Is electric potential a form of potential energy?

As I understand it, the concept of potential energy arises from analytical mechanics. Yet I often see the concept of electric potential $\phi$ introduced without mention of analytical mechanics. For ...
0
votes
0answers
30 views

Induced potential in a metal

My problem is as follows: A metal whose response is determined by the Thomas-Fermi equation: $(\nabla^{2}-\lambda^{2})V(r)=0 $ , occupies the $z<0 $ infinite half-space: show that the general form ...
1
vote
1answer
71 views

Deriving Voltage from Electric Field

I'm trying to derive the point charge equation for voltage by integrating the point charge equation for an electric field over distance ($dr$) traversed:$ \int (KQ/r^2)\cdot dr$ This is my ...
1
vote
2answers
105 views

Need of vector potential in quantum mechanics

I need your opinions. Why is the vector potential of a magnetic field important (or even necessary) to quantum mechanics? Why it has to be defined everywhere? Is there any fundamental reason you can ...
1
vote
1answer
32 views

Allowed energies for semi-harmonic oscillator

Question: If a particle is attached to a semi-harmonic oscillator (that is, for example, the spring is stretchable but not compressible) such that the potential $V(x)$ is infinity for $x\leq0$ and ...
0
votes
1answer
26 views

Capacitance per unit charge of three long rods, two of which are connected

Suppose we have three very long rods, each with diameter $a$, placed so that their "centers" form an equilateral triangle, with sided of length $d$. Two of the wires are connected with a thin wire ( ...
1
vote
1answer
29 views

Introducing cut-off in a renormalisation procedure for quantum mechanics

I've been reading a paper on renormalisation theory as applied to a simple one-particle Coulombic system with a short-range potential. In the process of renormalisation, the authors introduce an ...
0
votes
0answers
13 views

Low-momentum behaviour of a short-range potential

I've read the follow sentence in a journal article (arXiv preprint) which constitutes part of my coursework. As discussed in the previous section, the low-momentum behavior of any short-range ...
0
votes
1answer
28 views

Scattering from a potential, matrix elements of momentum eigenstates, and the Fourier transform [closed]

I am working on my last quantum homework and don't know where to begin with part (i) in this question 4. Do I need to use a product rule in the FT and use convolution? Not sure how to go about the ...
11
votes
6answers
668 views

Gibbs free energy intuition

What is Gibbs free energy? As my book explains: Gibbs energy is the energy of a system available for work. So, what does it want to tell? Why is it free? Energy means ability to do work. What is ...
2
votes
0answers
51 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 $n\geq 2$. ...
1
vote
1answer
34 views

Finding the potential between two spherical shells [closed]

How to find the potential in region $a<r<b$ I know that the general solution for Laplace's equation is $$V(r,\theta)=\sum_{l=0} \left[A_l r^l +\frac{B_l}{r^{l+1}} \right]P_l(\cos{\theta}).$$ ...
3
votes
1answer
154 views

1D Finite potential well: solutions with $\sinh$ and $\cosh$?

So I am studying the (one dimensional) quantum mechanical finite potential well defined by: $$ V(x) = \cases{0, &|x|>a\cr -V_0, &|x|<a} $$ where $V_0>0$ is a real number. I know ...
1
vote
1answer
36 views

Electric Potential-can anyone give the concept behind this?

Three points A, B and C lie in a uniform electric field (E) of 5 x 103 NC-1 as shown in the figure. Find the potential difference between A and C. I think there is some trick? How can the pd ...
0
votes
1answer
43 views

Why are the dineutron and diproton unbound?

It is known that there is no diproton and dineutron nuclei. Does this mean that two protons or neutrons are not actually attracted to each other? Even if the attraction was weak, wouldn't it cause ...
0
votes
0answers
18 views

What does it mean to charge a length of wire up to potential v?

I have to study the text "On the Theory of the Electric Telegraph," By William Thomson, 1855. I am having trouble gaining a conceptual understanding of the opening: "Let c be the electro-statical ...
0
votes
1answer
27 views

Potential Difference of a wire?

Imagine a circuit with only a 12 Volts battery and a wire connecting the ends of the battery. Point A and point B lies on the wire. What is then the potential difference between point A and B if the ...
1
vote
1answer
73 views

Bohr-Sommerfeld quantization for different potentials

Let's have Bohr-Sommerfeld quantization for one-dimensional case: $$ \int \limits_{a}^{b} p(x)dx ~=~ \pi \hbar (n + \nu ). $$ Here $p(x) = \sqrt{2m(E - U)}$, $a, b$ are turning points, and the area ...
1
vote
2answers
63 views

Semiclassical quantization of bouncing ball

Consider an elastically bouncing ball of mass $m$ and energy $E$. This has a triangular potential $$ V(x)~=~\left\{\begin{array}{ll} mgx & \text{if } x>0, \\ \infty & \text{if } x<0, ...
0
votes
0answers
14 views

Tersoff parameters

I am studying the tersoff potential i am trying to understand the physical meaning for each parameters in this potential. The development of Tersoff potential is a little fuzzy (several articles). ...
0
votes
1answer
37 views

Ignoring constant potential energy

The reason why constant potential energy terms are dropped is because the derivative of a constant is zero. And since force is the gradient of potential energy, constant terms won't change what the ...
1
vote
1answer
67 views

How to find an effective spring constant of a quadratic potential

If a potential energy is given like $U(r)=A^3/r^2+2B^3r$, how do I find the effective spring constant using Taylor Expansion? I compared spring constant $k$ to be equal to second derivative of ...
1
vote
1answer
45 views

Lagrangian of Non-Relativistic Charged Particle in a Magnetic Field

I'm trying to derive the Lagrangian for a non-relativistic charged particle under the influence of a magnetic potential. I'm assuming that $F=-grad(V)$ and so by the Lorentz force we have $-grad(V)=q ...
1
vote
0answers
26 views

Solving of one dimensional potential sets [closed]

is a set of 1D potentials which i need more examples and their solutions containing transmitting states, bounded states, scattering states and coefficients. I searched with 1D potential ...
1
vote
0answers
31 views

Flow in the strip $0 < x < \pi/2$, $y > 0$ [closed]

Could anyone please explain how to show that a complex valued function represents a flow? For example, how does one show that $\Phi(z) = \sec^2 z$, where $z = x + iy$ with $x, y \in \mathbb{R}$, ...
7
votes
4answers
449 views

Why the statement “there exist at least one bound state for negative potential” doesn't hold for 3D case?

Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal. However, today I'm doing a homework considering a potential like ...
0
votes
1answer
44 views

Electric field and potential between two charges [closed]

There are two point charges on the $x$ axis and $x'$ is a place where the potential, relative to infinity, is the biggest. Why is the electric field zero at this point?
-2
votes
3answers
89 views

Voltage in a parallel circuit [duplicate]

Why is voltage same across a parallel circuit? I mean what makes the voltage remain same across two resistors connected in parallel? If an electric heater is connected in parallel with a bulb and ...
-2
votes
1answer
91 views

Quantum mechanics: Finite square well problem

What will happen if the potential is less than 0, for instance $V(x)=-10eV$. Is this means there will be no bound states? Since solution to the time independent Schrodinger equation (those discrete ...
0
votes
1answer
26 views

Finding voltage between two points in space

If electric field vector is defines as : $\vec{E} = \frac{V_0x^2}{a^3} \vec{i_x} + \frac{V_0y}{a^2} \vec{i_y} $ where $V_0 $ and $a$ are known constants, $\vec{i_x}$ and $\vec{i_y}$ unit vectors of ...
2
votes
1answer
82 views

Inconsistency in the delta potential

I encountered an inconsistency in the one-dimensional delta potential. Suppose we have a one-dimensional infinitely deep square well from $-L$ to $+L$. We know the eigenstates are sine and cosine ...
3
votes
2answers
270 views

1D Infinite Square Box Discrete Energy levels but Continous Momenta?

In the 1d particle in the box the energy of the particle should be completely determined by the momentum of the particle that you observe correct? So how can you have discrete energy levels and a ...
3
votes
3answers
141 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 ...
0
votes
1answer
57 views

Introductory Quantum, trouble with this boundary condition and potential

Working on problem 2.40 from Griffiths but can't seem to understand the first boundary condition. We are given the potential $V(x) = \left\{\begin{matrix} \infty & x < 0\\ ...
0
votes
1answer
55 views

Scattering and bound States

So from my understanding, as long as $E>0$ you will have scattering states and these scattering states will always result in an imaginary $\psi$, but bound states can also have an imaginary ...
2
votes
1answer
104 views

Railguns and Gauge Invariance

Paul J. Cote and Mark A. Johnson of Benet Laboratories, Army Research, Engineering and Development Command wrote a series of short papers on the vector potential arising from their attempts to solve ...
0
votes
1answer
56 views

What is a Hulten potential?

What is the Hulten potential? When is it used? How is it derived? I vaguely heard about in the context of neutron synthesis / quantum mechanics. thanks
1
vote
1answer
98 views

Is the Gibbs-Duhem equation always valid?

The derivation of the Gibbs-Duhem equation from Wikpedia uses: As shown in the Gibbs free energy article, the chemical potential is just another name for the partial molar (or just partial, ...