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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In a positively biased PN junction, where do the injection carriers come from?

I am not quite understand i-v character of PN-junction diode. Here is the model in textbook. The PN junction diode can be divided into three regions. They are One depletion region near the PN ...
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29 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 ...
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73 views

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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1answer
46 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 ...
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328 views

Child-Langmuir Space Charge Law for Non-Zero Cathode Potential (Non-Zero Initial Electron Velocity)

I'm trying to reconcile some conflicting results that I've found in publications that address the idea of the current in a vacuum diode in the case where the cathode has a non-zero potential, in other ...
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81 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 ...
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57 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 ...
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239 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, ...
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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 $n\geq 2$. ...
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39 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 $V\left(\phi\right)$ ...
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65 views

WKB approximation in two dimensions

Does anybody know how to implement the WKB approximation for the two-dimensional Schrodinger equation with a harmonic oscillator potential: $\frac{1}{2}\Biggl[-\biggl(\frac{\partial^2}{\partial ...
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366 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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55 views

What is (or where can I discover) the Burke Potential?

I have very much enjoyed William L. Burke's Applied Differential Geometry. Reading around on the web it seems that he discovered something which is called the (retarded) Burke Potential, but I have ...
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80 views

The particle mesh ewald method in two dimensions

I am attempting to implement the particle mesh ewald method (http://dx.doi.org/10.1063/1.470117) in two dimensions. I am wondering what needs to be changed in the method from three dimensions to two ...
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83 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 ...
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39 views

What is “W external” and “W internal” in Energy conservation law?

When I solve the energy conservation problem, I am confused when I have to make the term positive or negative. For example, someone throws a ball right up to the ground with velocity, $v$. The ball ...
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51 views

What is the physical meaning of the norm of the electromagnetic four-potential?

In SI units this would be $\frac{1}{c^2}\phi^2 - A_x^2 - A_y^2 - A_z^2$. Is this just not a physically meaningful quantity at all because it's not gauge invariant?
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34 views

Nonlocal interaction effects on bose-einstein condensates

I'm studying an interacting bose-einstein condensate using the energy functional proposed in this paper K. Huang, C.N. Yang, Phys. Rev. 105 $$ E\left[\phi\right] = \int d^3\vec{r} ...
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121 views

The Effect of Tortoise Coordinates

Referring particularly to http://arxiv.org/abs/hep-th/9909056 in regard to the wave equation for Schwarzschild-AdS black holes (p.4), I'm trying to understand tortoise coordinates. So starting ...
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28 views

Surface potential resulting from the charge transfer between insulator and conductor

Common non-contact electrostatic voltmeters are used to measure the surface potential. Imagine we place a charged insulator on top of the conducting plate (insulated from the surrounding) and measure ...
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74 views

Quick question on sketching wavefunction in well

Usually for an infinite well, the sketch for n=3 level is this: Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than ...
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108 views

Particle in a higher-dimensional box with an attractive delta potential

Suppose you have a particle in the box $[0,L]^d$, with an attractive Dirac delta potential $-\delta_{\vec w}(x)$ at $\vec w$. How do you solve the Schroedinger equation for this system? In the case ...
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69 views

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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582 views

Scattering on delta function potential

Suppose a particle has energy $E>V(+/-\infty)=0$, then the solutions to the Schrodinger equation outside of the potential will be $\psi(x)=Ae^{i k x}+Be^{-i k x}$. How can one show or explain that ...
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132 views

An electron is subjected to an electromagnetic field using the canonical equations solve

So I was given the following vector field: $\vec{A}(t)=\{A_{0x}cos(\omega t + \phi_x), A_{0y}cos(\omega t + \phi_y), A_{0z}cos(\omega t + \phi_z)\}$ Where the amplitudes $A_{0i}$ and phase shifts ...
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19 views

What justification is necessary for convolutional variational principles to be considered legitimate?

I recently asked a related question and was interested in why/or why we cannot use convolutional variational principles in practice or in theory. Summarizing the points I made in the earlier post: ...
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22 views

Is it possible to get the (Pauli) repulsive term in the Lennard-Jones potential from theoretical considerations?

Title says it: Is it possible to get the form of the (Pauli) repulsive term in the Lennard-Jones potential from theoretical considerations, or is it purely found experimentally through fits?
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31 views

Potential difference and voltage

Is potential difference between two points the voltage? (or) Is voltage the potential difference between two points? (or) Are they both the same?
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32 views

How would you define a difference in potential?

I'm currently in 12th grade, and am required to write an essay about physics and biology. The topic of the essay is the artificial brain (with the researches of the Human Brain Project in Switzerland ...
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30 views

Why does charge build up at the boundary surface of two media?

On a homework problem, we are asked to to use the first two Maxwell equations, $$\nabla\cdot \mathbf{B} = 0$$ $$\nabla \cdot \mathbf{D} = \rho$$ to show that along the boundary surface of two ...
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30 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?
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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 ...
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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 ...
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21 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 ...
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15 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). ...
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27 views

Meaning of negative effective range

In a case of a square-well potential the effective range and the scattering lenght depends on the characteristic parameter of the potential (see the explicit formula here, eq. 25a,25b ) and the plot ...
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39 views

What is the functional shape assumed by a flexible rod?

Be L a flexible rod. Say that it is very difficult to significantly stretch it, so that we can uniquely identify a point on it by a parameter $l \in [0, L]$ where $L$ is its length. Be $C$ a set of ...
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135 views

Finite Square Well Inside an Infinite Square Well

Ok here's a potential I invented and am trying to solve: $$ V(x) = \begin{cases} -V_0&0<x<b \\ 0&b<x<a \\ \infty&x>a \\ \end{cases}$$ and $V(-x) = V(x)$ (Even ...
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58 views

Variation of Electrostatic Potential with Distance in a Uniform Field

I came across this question in a problem book: If a proton is released from rest in a uniform electric field, does the electric potential at those points where the electron moves increase or decrease. ...
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67 views

Infinite Round Square-Well zeroes of Spherical Bessel function

Consider a potential well where the potential is zero within a spherical well of radius a centered on the origin. Taking $a$ as our length scale and $\hslash^2/(2ma^2)$ as our energy scale, we gain ...
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30 views

Particle in a box under harmonic driving

Is the particle in a box under harmonic driving electric field solvable analytically? Here is the Schrodinger equation: $$ i\frac{\partial \psi(x,t)}{\partial t}=\left[-\frac{1}{2} ...
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18 views

Physics of a conductor gaining potential

Working on electrical engineering but thus far, the physics stack has proven to be a better place to read and ask questions in order to develop a better overall understanding. I am currently waist ...
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53 views

Electric Potential Change

Imagine we have a conductor in the shape of a sphere with charge $Q$ on it. The conductor is not grounded. There is an associated potential $V=\frac{Q}{4\pi\epsilon_0 R}$ at and in the sphere, where ...
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30 views

Looking for Solutions to Symmetric Potential

I'm a little confused on the basic method of finding a separable solution to a give potential distribution. If we have a symmetric potential, say it hits zero and $-a$ and $a$, constituting two sides ...
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497 views

Vector and scalar potentials of plane wave

Consider a simplest 3D solution of Maxwell's equations: $$\vec B=\vec e_z \cos\left(\frac{2\pi}{\lambda}(ct-x)\right),$$ $$\vec E=\vec e_y\cos\left(\frac{2\pi}{\lambda}(ct-x)\right),$$ and ...
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71 views

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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297 views

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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243 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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186 views

Wave equations for two intervals at Potential step

Lets say we have a potential step as in the picture: In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$. Let me ...
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39 views

Is it easier to determine the number of states with raising/lowering operators or using scattering?

A particle is bound by $$V(x) = \begin{cases}\infty,& x <0 \\ \frac{-32\hbar^2}{ma}, & x\le a \\ 0, & x \le a\end{cases}$$ a) how many states are there? i'm attempting ...