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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Integers, energy levels, and wavenumbers for a particle in a 2D box

I have written a program that allows the user to plot the energy vs the wave number of particle in a 2D box, depending on what values for the integers $p$ and $q$ they desire. The energy $E_{p q}$ ...
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What is a potential in De-Broglie-Bohm theory?

As I have so far understood, the De-Broglie-Bohm theory is based on two equations: The Schrödinger equation. The Guiding equation of the De-Broglie-Bohm theory. In the Schrödinger equation (as ...
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60 views

A question about electric field

I would like to understand why is it the charge density while dealing with currents is $\mathop{\mathrm{div}}(E)/4\pi$, while when dealing with insulators is $-\mathop{\mathrm{div}}(E)/4\pi$? Thank ...
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Electrical potential difference?

What is the electrical potential difference and why we have to talk about a difference and not about the electrical potential itself? What is the electrical potential difference in practical terms ...
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180 views

Are $G$, $F$ and $H$ (thermodynamics potentials) extensive quantities?

Internal energy $E$ is an extensive quantity for most systems. But energy extensivity is not valid in systems with long-range interactions, like gravity (e.g. in astrophysical systems). For extensive ...
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174 views

How do aspherical gravitational monopoles look like?

I was recently pointed by laboussoleestmonpays to a beautiful paper from some time ago, Aspherical gravitational monopoles. Alain Connes, Thibault Damour and Pierre Fayet. Nucl. Phys. B 490 no. ...
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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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When is energy discrete/quantized for a potential well?

Specifically, my question is: Should one expect energy quantization for a particle in the following potential well? More generally, how can one tell whether or not energy should be ...
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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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What is the meaning of $U''(x)=0$?

Most potentials with a minimum can be described approximately as a harmonic oscillator. So the procedure is to Taylor expand $U(x)$: $$U(x)=U(0)+U'(0)x+\frac{1}{2}U''(0)x^2 +...$$ If we suppose ...
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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 ...
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Bound state in a potential well?

Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html It says: This means that the solutions separate into even parity and odd parity states. We could have guessed this from ...
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Which number should I suppose to $a$ (width of well) and $m$ (mass of particle) in potential well problem? [closed]

I tried to plot a complete of state functions of potential well problem but graph was so weird. I thought a cause was variables a and ...
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The criteria for potential flow theory

I am learning aerodynamics. In this course a potential flow is denoted that a flow in which the rotation is zero everywhere. But the book told me that we can add vortex into a flow field, and we can ...
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Wave function interaction

If you have two or more wave functions that represent electrons or other charged particles, how would the force on one be calculated based on the charge of the others.
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Anharmonic oscillators: why is $F=-k x-k' x^3$, with no quadratic terms?

The equation of motion of a general anharmonic oscillator includes a position-dependent force that can be expanded in a Taylor series as $$m\ddot{x}+2\mu\dot{x}+k_0+k_1x+k_2x^2+k_3x^3\ldots=F.$$ I ...
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137 views

Is self gravitation theoretically impossible?

Is it theoretically possible to create some system such that the energy distribution creates a gravitational potential offset from its center of mass (or energy?) so that the body continually 'falls' ...
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667 views

Alternative derivation for the capacitor energy equation [closed]

I hope this is the right place for this kind of post. A friend is trying to derive the equation for the energy stored in a capacitor by analysing the change in potential on one plate when the ...
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142 views

How to understand dynamics $\dot x_i=\partial_jA_{ij}$ from skew-symmetric potential $A$?

We speak of a dynamical system with a potential if there is a scalar possibly depending on coordinate such that the vector field is exactly the (negative) gradient of the potential. That means each ...
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A satellite in orbit fires it's engines for a short interval. Is the new orbit closer or further away?

A satellite is in a circular orbit when its engines turn on to exert a small force in the direction of the velocity for a short time interval. Is the new orbit further or closer to the Earth? The ...
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Finding out the potential [closed]

According to me, if we want to find out the potential the the equation will be, $$dV = \int \frac{dQ}{4 \pi \epsilon_0 x}$$. But the answer is given is on the basis of $$dV = \int \frac{dQ}{4 ...
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183 views

Quadrupole potential generation in Paul traps

I am currently getting familiar with the concept of the Paul trap and the underlying physical principles. I do understand what kind of potentials are needed to trap charged particles, e.g. for the 3D ...
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Slight variation to method of images

Suppose a point charge $q$ is located at $(x=0,y=0,z=d)$, and that along the $x$-$y$ plane is a infinite plate of potential $V = 0$. Then the method of images solves Laplace's equation for the ...
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Strong Newton's third law of action and reaction: Mathematical Interpretation

According to the strong law of action and reaction for internal forces(Goldstein): "$F_{ij}=-F_{ji}$ and the forces lie along the direction joining the particles." Now consider the statement If ...
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Infinite Wells and Delta Functions

In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of ...
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Gradient of the potential originated from two similar magnetic vector potentials is not the same

The magnetic vector potential $\textbf{A}$ can be defined up to a gradient of a field. Adding or subtracting such gradient should not change the physics of the problem. The same reasoning is applied ...
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410 views

Canonical momentum Velocity dependent Lagrangian

I have a homework problem wich I think I'm on the verge of solving but need help with some relations: Show that if the potential $U$ in the Lagrangian contains velocity-dependent terms, the ...
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531 views

Transparence of an infinite square well? [closed]

What does it mean by an infinite square well being transparent? I have been doing the calculation of the infinite square well and I came up with an answer $T = 1$ where $T$ for Transmission ...
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799 views

How does charge flowing between emf terminals reduce voltage difference?

I'm currently learning what electromotive force is and while reading my book's description of an ideal source of emf, I had difficulty understanding what these sentences mean: The nonelectrostatic ...
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1answer
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How to find the wavefunction that solves an infinite square well with a delta function well in the middle?

Solutions for the wavefunction in an infinite square well with a delta function barrier in the middle are easily found online (see here for an example). I am wondering what the wavefunction is for an ...
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1answer
478 views

Quantum Mechanics and the Airy Function, the physics of the turning point

I'm working with the Airy function, and the book states at $x=0$ is a turning point, and there are two very different behaviors on either side. In general what a does a turning point mean in ...
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392 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 ...
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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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251 views

Stable equilibrium given force

If a particle moves under the influence of a resistive force proportianal to velocity and a potential $U$, $$F(x,\dot x)=-b\dot x-\frac {\partial U}{\partial x}$$ Where b>0 and ...
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758 views

Quantum mechanics potential barrier problem [duplicate]

While reviewing some quantum mechanics, I cam across a very interesting situation. For a potential barrier, if a particle has an energy $E$ less than the potential barrier $V_0$, it is possible to ...
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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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Does the Lennard-Jones force equation give its answer in Newtons?

I'm trying to do the dimensional analysis of the Lennard-Jones force to work out what units are being used in my MD simulation. The lennard Jones force is given as the negative derivative of the ...
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Why is Energy = Voltage x Charge, and how to prove that?

As you know the equation $\mathbf{E=V\times Q}$. Where: $\mathbf E$ is the energy measured in joules, $\mathbf V$ is potential difference (Voltage), $\mathbf Q$ is the charge. So my qustion is: ...
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Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be ...
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Wavefunction as a combination of two stationary states - how to find those states?

Lets say we have a particle in a infinite square well which has a wavefunction like this ($A$ is some constant and $d$ is the width of the well): \begin{align} A\left[ \sin \left(\frac{2 \pi ...
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Dirac Delta Potential and bound/scattered states

Why does the attractive Dirac Delta distribution (function) potential $V = \alpha\delta$(x) (for negative $\alpha$) yield both bound AND scattered states? Is this due to the definition of the Dirac ...
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287 views

exponential potential in physics

given the differential equation $$ -\hbar^{2}D^{2}y(x)+ae^{bx}y(x)=E_{n}y(x) $$ here $ D=d/dx $ derivative are there examples in physics where this potential appears ??, i know how to solve it but ...
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336 views

Understand equations of a conducting sphere

Can somebody explain to me, when the following two equations (equations 2.48 and 2.50 in this document) are applicable and what $\Phi_s$ and $\Phi$ actually are? The thing is, I want to find general ...
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Frank-Hertz experiment setup

The usual schematic representing the setup of Frank-Hertz experiment is the following: However, sometimes, you can see a bit different schematic: My question is: what function does $V_{G_1K}$ ...
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Conditions of applicability of potential flow about an airfoil

In many cases the flow about an airfoil is calculated by solving the Laplace equation, (for example in the Hess-Smith panel method). If the velocity field is irrotational and its divergence its zero, ...
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How to find electric scalar potential of infinite wire with Poisson/Laplace equation?

I though it will be easier then calculating the electric field and then integrating, but I am stuck. lets say we have an infinite wire, charged $\lambda$ per unit of length and its located at the ...
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Is electron volt an alternate unit for electric potential? [closed]

My question is: Can an electron volt be considered an alternate unit for electric potential?
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Is there an equivalent of a scalar potential for torques?

For a given scalar potential $V$, it is known that the corresponding force field $\mathbf{F}$ can be computed from $$ \mathbf{F} = -\nabla V $$ Suppose a rigid body is placed inside this ...
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Why doesn't a quantum particle in an attractive 1D potential accumulate at the center?

I have two questions regarding (possibly counter intuitive results) Schrodinger equation and its application to two (strictly hypothetical) scenarios. Consider the 1D potential $V(x) = - ...
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Dimensions in lagrangian potential

According to Mankowski flat space dimensions We can write, $$L= \int \text{dt} \text d^d{x} \left[ \frac{1}{2} \dot\phi^2 - \frac{1}{2} \left(\frac{\partial \phi}{\partial r} \right)^2 ...