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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Continuity & smoothness of wave function

Is there anything physical that enforces the wave function to be $C^2$? Are weak solutions to the Schrödinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't mention ...
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Why are thermodynamic potentials minimised?

Why is it that, at equilibrium, certain potentials are minimised? That is, for a system at constant temperature and pressure, the Gibbs free energy is minimised, and for fixed volume and temperature, ...
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In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?

A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. Is there a one to one correspondence between the potential and its spectrum? If the answer ...
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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.
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Time-independent Schrödinger function: If the potential $V$ is even, then the wave function $\psi$ can always be taken to be either even or odd

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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Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
Mark Eichenlaub's user avatar
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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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What is the difference between electric potential, electrostatic potential, potential difference (PD), voltage and electromotive force (EMF)?

This is a confused part ever since I started learning electricity. What is the difference between electric potential, electrostatic potential, potential difference (PD), voltage and electromotive ...
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When Eigenfunctions/Wavefunctions are real?

When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real? What happens in 1D case like the finite ...
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I don't understand what we really mean by voltage drop

This post is my best effort to seek assistance on a topic which is quite vague to me, so that I am struggling to formulate my questions. I hope that someone will be able to figure out what it is I'm ...
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What exactly is a bound state and why does it have negative energy?

Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)? Why, when a stable ...
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Why are the dineutron and diproton unbound?

It is known that there are no diproton or 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 ...
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Why the statement "there exist at least one bound state for negative/attractive 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 this:$...
an offer can't refuse's user avatar
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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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Direction of $d\mathbf{l}$

A solid sphere has charge $q$ and radius $R$. Find the potential at a point a distance $r$ from the center of the sphere where $r>R$, using infinity as the reference point. My attempt: From Gauss'...
Siddhartha's user avatar
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When does the $n$th bound state of a 1D quantum potential have $n$ maxima/minima?

In Moore's introductory physics textbook Six Ideas that Shaped Physics, he describes a set of qualitative rules that first-year physics students can use to sketch energy eigenfunctions in a 1D quantum-...
Michael Seifert's user avatar
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2 answers
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Potential for a general fictitious force?

In a general non inertial system four fictitious forces arise: Coriolis Force, centrifugal Force, azimuthal Force, "translational" Force (due to linear acceleration of the origin of the system) I ...
Federico Toso's user avatar
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Hexadecapole potential using point particles?

We can get monopole $1/r$, dipole $1/r^2$, quadrupole $1/r^3$ and octupole $1/r^4$ potential falloff by placing opposite point charges at the corners of a point, line, square and cube, respectively. ...
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Degeneracy in one dimension

I'm reading this wikipedia article and I'm trying to understand the proof under "Degeneracy in One Dimension". Here's what it says: Considering a one-dimensional quantum system in a ...
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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 ...
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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 $...
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17 votes
3 answers
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What is a gauge in a gauge theory?

As I study Jackson, I am getting really confused with some of its key definitions. Here is what I am getting confused at. When we substituted the electric field and magnetic field in terms of the ...
Roshan Shrestha's user avatar
12 votes
3 answers
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Pn junction voltage drop?

This image from wikipedia, explains that there occurs a potential drop across a pn semiconductor junction, and an electric field confined to the depletion region. I already know the reason for the ...
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Why is there an "electric" potential drop across the resistor?

An electric potential difference is created when two charges are separated. In a capacitor, there is a clear accumulation of opposite charges on the two separated plates, therefore work has to be done ...
Aravindh Vasu's user avatar
21 votes
1 answer
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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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Why is the work done on a charge calculated from infinity?

Why is the work done on a charge calculated from infinity to a point? Why not from one particular point to other?
Anish Kumar's user avatar
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4 answers
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How to obtain large order perturbation series for cubic anharmonic oscillator?

Consider the potential $$V(x)= \frac{x^2}{2} + gx^3.\tag{1}$$ Then the time-independent Schrödinger equation becomes $$\left(-\frac{1}{2}\frac{d^2}{dx^2} + \frac{x^2}{2} + gx^3 \right)\psi = E(g) \psi....
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The meaning of potential in Bohm-Aharonov experiment

The Bohm-Aharonov experiment involves a magnetic field inside a cylinder which is zero outside that cylinder. Nonetheless it affects the electrons moving outside the cylinder. The explanation for this ...
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Deriving the Lorentz force from velocity dependent potential

We can achieve a simplified version of the Lorentz force by $$F=q\bigg[-\nabla(\phi-\mathbf{A}\cdot\mathbf{v})-\frac{d\mathbf{A}}{dt}\bigg],$$ where $\mathbf{A}$ is the magnetic vector potential and ...
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What maintains constant voltage in a battery?

I know there's lots of questions that address similar situations, (Batteries connected in Parallel, Batteries and fields?, Naive Question About Batteries, and the oft-viewed I don't understand ...
Andres Salas's user avatar
14 votes
3 answers
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Motivation for Potentials

This is a hypothetical question about "pedagogy". Let's say I am trying to take someone who has just a very small amount of knowledge about Newtonian mechanics and convince them that the Lagrangian ...
Jonathan Gleason's user avatar
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2 answers
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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 ...
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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 ...
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1 answer
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How to formulate variational principles (Lagrangian/Hamiltonian) for nonlinear, dissipative or initial value problems?

Although this questions is very much math related, I posted it in Physics since it is related to variational (Lagrangian/Hamiltonian) principles for dynamical systems. If I should migrate this ...
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1 answer
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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 ...
Jonathan.'s user avatar
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19 votes
6 answers
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Is the harmonic oscillator potential unique in having equally spaced discrete energy levels?

I was wondering if the good old quadratic potential was the only potential with equally spaced eigenvalues. Obviously you can construct others, such as a potential that is infinite in some places and ...
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Reflectionless potentials in quantum mechanics

Scattering on potential $$V(x) = -\frac{(\hbar a)^2}{m}\text{sech}^2(ax)$$ with 1D equation of Schrodinger is famous problem. It is dealt with in Problem 2.48 of Griffiths book or online here. It is ...
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4 answers
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Force as gradient of scalar potential energy

My text book reads If a particle is acted upon by the forces which are conservative; that is, if the forces are derivable from a scalar potential energy function in manner $ F=-\nabla V $. I was ...
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Is there any potential associated with magnetism?

Can anybody please tell me if magnetism is a conservative force or if there is a field associated with it? How to reason? One thing I know is that the work done by a magnetic force is equal to $0$.
Amogh's user avatar
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How can there be a voltage across an inductor if the voltage through any conductor is zero?

It's commonly taught that the electric field in a conductive material is zero. Hence the voltage through a perfectly conductive material is zero. I however when learning about inductors in physics ...
Nathan Rotta's user avatar
7 votes
3 answers
9k views

Capacitance of a single charged plate?

Lets say we have a single plate that has a charge of $+Q$ on it. A plate with charge $-Q$ is infinite distance away. Will the plate with $+Q$ have a capacitance associated with it? Why or why not? I ...
John Burgerman's user avatar
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3 answers
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Is electric potential always continuous?

In electromagnetism, we say that any conservative electric field $\vec{E}(\vec{r})$ is associated to a scalar potential $V(\vec{r})$ such that $\vec{E}(\vec{r}) = -\nabla V(\vec{r})$. If the electric ...
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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 ...
user20486's user avatar
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3 answers
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Higher order derivatives - Equation of motion

One possible starting point to create a physical theory is the Lagrangian $L$. There we assume that the variation of the action $\delta S = \delta \int_{-\infty}^\infty dt \ L = 0$. In classical ...
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Point charge potential (sign problem)

I'm a bit embarrassed, but I'm not able to compute the electric potential at point $P$ (at a distance $R$ from the origin) generated by a positive unitary point charge in the origin with the right ...
wiso's user avatar
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2 answers
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How to calculate eccentricity of a planet via energy?

The relative distance of a planet moving around the sun is found to be: $$r(\varphi) = \dfrac{\kappa}{1+\varepsilon\,\cos(\varphi)} \quad \text{where} \quad \kappa = \dfrac{L^2}{G\,{m_p}^2\,m_s} \quad ...
Leon's user avatar
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20 votes
7 answers
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Why does a Resistor cause a potential drop?

I need to know the underlying physics of what exactly happens different with the electric field in the resistor than in superconducting wires. Why is it that when I connect a resistor, potential drops ...
Silver's user avatar
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16 votes
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Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
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How can the electric potential be zero at a point where the electric field isn't, if that field can give a test charge kinetic energy?

Say we have 2 charges set up like above. Why is $V_3=0$ ? I can understand mathematically that the scalars fields cancel out, but I don't understand it physically. If I place a positive charge in ...
John Hon's user avatar
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13 votes
6 answers
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Why is the electric field perpendicular to every point on the surface of a conductor?

I am reading Berkeley Physics Course, Volume 2 (Electricity and Magnetism by Edward M. Purcell). I am in chapter $3$, page $92$, and the book discusses conductors. The following is from the book: ...
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