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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.

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Fourier transform of a scatering potential

The Fermi golden rules states $$ \Gamma(\vec{k},\vec{k}') = \frac{2\pi}{\hbar} \left| \left \langle \vec{k}|V|\vec{k}' \right \rangle \right|^2 \delta(E(\vec{k})-E(\vec{k}')) \, .$$ Many places (for ...
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What is the main point in defining electric potential?

What I mean is that as the electric field is a necessity for us to define it because it has practical applications and similarly we need electric potential energy because it is the energy we require ...
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Potential from scattering matrix [duplicate]

Given a scattering matrix, is there a procedure to find the potential from the scattering matrix? I think there should be a way as the scattering matrix holds the information of the boundary ...
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How can I calculate the time it takes a pendulum to hit the lowest point again? [closed]

I'd like to calculate how long it takes for a pendulum to reach the lowest point again. I guess there are two different cases: When the pendulum is descending When the pendulum is climbing: I guess ...
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Finding the potential for a given Hamiltonian

Background: So I know from my lecture that if I am given a wave-function, which describes a particle and a potential V(x) in which the particle is in, I can use V(x) in the time-independent ...
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What are wave-functions in QM. corresponding to?

I was learning about a particle trapped in a double well potential $$V(0) = \infty, V(x1)=\infty$$ which can be described by $\psi_n$ for n=0,1,...,$\infty$ with corresponding Energies $E_n$. Just ...
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E greater than V [closed]

Show that E must exceed the minimum value of V(x) for every normalisable solution to the time-independent Schrödinger equation? This question was given to be proved in David Griffith's ' ...
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Infinite square well: wall with infinitesimal thickness

Given an infinite square well, it doesn't matter how thick the wall is, the particle is trapped inside the two walls. If we make the wall of arbitrarily small but finite thickness, the particle is ...
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Potential energy of a charge in a magnetic quadrupole field

I have a charged particle of charge $q$ that moves with velocity $\vec{V}$ from a position $\vec{r}$, inside a magnetic quadrupole field of the form: $$\vec{B}=B_{0}(x,y, -2z)$$ The Lorentz force acts ...
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Physical meaning of potential in heat equation

I'm working on the mathematical theory of parabolic equations. The prototype of such equations is heat equation given as follows : Let $\Omega$ be a bounded region of the space and $T>0$ a fixed ...
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Interpretation of the magnetic potential ($A$-field) in the quantum mechanical probability of current

The probability of current in quantum mechanics when the is a magnetic potential, A, is defined as: $$\boldsymbol j=\frac{1}{2m}(\psi^*\hat{\boldsymbol p} \psi-\psi\hat{\boldsymbol p}\psi^* -2q{\...
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Misconception about flow of charges

Let's say I have a 5V battery connected in the manner shown in the diagram. I've tried this setup with all sorts of things like pouring brine(salt water) into the soil to decrease its resistance so ...
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Why did we take gradient outside the integral sign in Scalar potential derivation?

I tried to understand the reasoning given in it but I couldn't understand it. It says that "as the gradient operation involves x and not the integration variable x', it can be taken outside the ...
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Potential Difference of a battery - What does it mean?

I have studied current electricity for a while now. When I look back at basic concepts, I am quite clear about what current, electron, resistance is. But I cannot imagine about the potential ...
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Potential difference of resistors in parallel linked systems

Before the question I want to explain somethings to see if I understand anything wrong please tell me if im wrong: When there is a Potential difference on a system then the electrical charge will move ...
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Help me make sense of the spectrum for the quantum wave function of an infinitely hard equilateral triangle

I'm trying to solve the spectrum for a equilateral Tetrahedron with infinitely hard walls. My first guess is to sum up a infinite amount of separable solutions to match the boundary conditions on the ...
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Can electric potential be discontinuous?

I am studying the following problem, which is 9.11 of "Modern Electrodynamics" by Zangwill. The idea is that you have a wire attached to a perfectly conducting sphere (radius $a$) buried into the ...
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Screening of a coulomb-like potential

Imagine that we have a potential in the form of: $U(r) \propto \frac{1}{r^n}$ in a 2D system, with the high concentration of particles interacting with the above potential. How do you find the ...
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Why do we assume simply connected domains and continuously differentiable fields in electromagnetism theory?

In many textbooks, including Griffiths', they erroneously claim that a field is irrotational if and only if it is conservative (there exists a scalar potential). This is true only if the domain of ...
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Why can't a particle penetrate an infinite potential barrier?

I am studying basic quantum theory. My question is: Why can't a particle penetrate an infinite potential barrier? The reasoning that I have applied is that particles under consideration have finite ...
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1answer
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Is potential instantaneous, unlike fields which take time to alter depending on their mediators?

If there's a Charge distribution 4 Light-years away, static, we have a distinct value of Electric Field and Electric Potential where I'm measuring it through some wack-a-doodle apparatus at my home on ...
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How to understand Kirchhoff's Voltage Law?

I'm having a hard time trying to understand why Kirchhoff's Voltage Law is true. I looked for an answer on the forum but I couldn't find a convincing one. So my question is : How to "physically" ...
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What is meant when we say “any solution is *the* solution” due to the uniqueness theorem?

I understand the proofs for the uniqueness theorems in electrostatics, but I'm having trouble understanding their application to problem solving. A classic example is a system of concentric shells of ...
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Liénard-Wiechert potential of a charged infinite sheet uniformly translating parallel to itself

This question is motivated by the model used in The Feynman Lectures on Physics Vol II Section 18-4. In the model there are two plane sheets extending infinitely in both their dimensions. Each has a ...
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Thermodynamic Stability - Convexity - Concavity of Thermodynamical potential

The thermodynamic stability principle requires convexity of the internal energy upon all of its independent variables. When we pass through the Legendre transforms to build all the other ...
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Could someone explain what is a potential?

In many part of physics, me talk about potential (electrical potential, gravitation potential, elastic potential...). All those definition looks very different, and I would like to know how all those ...
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Does a particle with infinite energy escape an infinite well?

Currently, my modern physics class is going over particles in finite and infinite wells, general quantum formalism, and tunneling. What happens to a particle as it gains an infinite amount of energy? ...
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How does a piece of wire know there is a voltage potential different?

Imagine water molecules inside a water pipe is moving due to difference in pressure, this pressure can be due to difference in gravitational potential or external force like somebody squeezing at one ...
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Is it possible to draw a potential landscape for this system?

Attention: The question was modified for numerical solution. (see Update 2) I have the following system of differential equations: \begin{align} \dot x & = -x+F(a\,y+b),\\ \dot y & = -y +F(...
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Circumstances that might happen in Hall-effect experiment

In Hall-effect experiment, is it possible that no transverse potential difference will be observed? Under what circumstances might this happen?
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Magnetic vector potential on a semicircle wire

If you're trying to calculate the magnetic vector potential A on a semicircle wire at an arbitrary point P on the other semicircle, is their a difference in method if you are calculating it on a ...
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1answer
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Defining potential of the ground

In electronics, it is customary to define the potential of ground (thinking the Earth as a large conductor) as zero. Is this consistent with the fact that the Earth has a net electric charge that is ...
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Grounded parallel plate capacitor

What will be the charge distribution if a parallel plate capacitor, which is not connected to any battery, is given charge on one plate(say Q on the left plate) and is grounded on the outer side of ...
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Spring constant and dispersion relation

In order to calculate the dispersion relation (i.e $w(k)$) for the electrons and protons, I used the following relations: $ E = ℏω$, $p = ℏk$, and I substituted them in this formula for energy: $E = ...
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How do I determine the accuracy of this two-dimensional potential field?

Let's say I want to solve this problem. I know the values on the boundaries and I guess an initial solution on the rectangular grid inside these boundaries, see figure below. Potential=10 on ...
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Taylor expansion for a double well/perturbed infinite square well

I'm trying to estimate the ground state energy for a perturbed infinite square well directly. The potential is piecewise constant $$V(x)=\begin{cases}&\infty, \qquad x<-a/2\\ &0 \qquad -a/2&...
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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 \...
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How a battery maintains the current in the circuit? [duplicate]

How a battery maintains the current in the citcuit? Iwant to know each and every step of this process mathematically and theoretically also.
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Will the expressions for magnetic vector potential and Biot-Savart law hold at points on line current?

If we have a line current, will magnetic field be defined at points on the line? Will the expressions for: $(1)$ Magnetic vector potential $$\vec{A}=k\int^l_0 \dfrac{\vec{dl}}{r}+\nabla f(x,y,z)$$ $(...
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Grounding and equipotential lines

In my textbook it says: One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor. This implies that a conductor is ...
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Field between 2 electrodes experiment

We were asked to conduct an experiment that is as follows: Connect 4.5V constant voltage across 2 electrodes of thin Cu wire, dipped in a tub of copper sulfate solution. A needle is connected to a ...
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impossible Poisson's ratio of Lennard-Jones potential type solid (cubic cristal for example), or any potential depending on $r$

We know (for instance : https://en.wikipedia.org/wiki/Poisson%27s_ratio ) that the Poisson ratio is $\nu=1/2-Y/(6B)$, with $Y$ the Young modulus and $B$ the bulk modulus. Let's assume we have a ...
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Gravitational potential of an approaching mass

Let $\Phi(0, t)$ be the gravitational potential at the origin and $t$ the clock ticking at infinity, i.e. not influenced by any gravitation. Let a mass $m$ approach the origin with constant velocity ...
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Question about fundamental states on an finite well

My question is the following, when we search for the bound states a finite well potential we have solutions symmetric and antisymmetric so we get two families of solutions. In this case, the ...
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3answers
51 views

How do we deduce the vector potential for a constant magnetic field?

How do we show that for a constant magnetic field $\vec B = const$, the vector potential is $\vec A = \frac12 \vec r \times \vec B$?
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Interactions between “particles” to prevent diffusion and to cause phase segregation

The free energy of particles reads, if we assume no internal energy : $\tilde f(c)= \frac{f(c)}{k_bT}=-c \, ln(c)-(1-c)\, ln(1-c)$, with $c$ the concentration. If we had a term $F(c)$ for the ...
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What is the difference between the voltage in the electrical circuit and electrostatics?

In electrostatics it depends on the distance from the charges, should it also be in the circuit? But in practice, the voltage depends on the resistance, for example on a resistor. And the distance ...
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Electron travelling through a step potential from $V_0$ to 0

Most of the time you discuss the step potential case when $E>V_0$, you consider an electron (or a beam of electrons) travelling from a region of space $x<0$ in which $V=0$, to a region $x>0$ ...
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How can Young modulus depend on the geometry of the item & Lennard Jones (question related to an older one)

In the question Young's modulus and geometry of test material, the answer was that it cannot play any role. Nonetheless, for the Lennard-Jones solid, in many places the Young modulus is given as : ...
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Confusion in work done in moving charge to infinity from center of conductor

A point charge $q$ is at center of spherical conducting shell of inner radius $a$ and outer radius $b$. Find work done in moving charge to infinity. The answer (given in book) is: $$W = \frac{q^2}{8\...