# Tagged Questions

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

91 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 ...
66 views

47 views

### What is the charge density for line and surface charges?

In electrostatics it is common to see line, surface and volumetric charges being described differently. A line distribution is a function defined on the line, a surface charge distribution is a ...
44 views

### Method of image charges — Why is a *grounded* plate needed?

In the classic image charge problem of a charge $q$ above an infinite grounded plane, it is well known that the field lines essentially behave as though there were a negative charge behind it, and the ...
112 views

### Guess the wave function in a given potential

Are there any techniques in guessing the ground state wave function in any given potential? For example, for a given potential like $$\frac{1}{1-x^2}$$ or $$\frac{1}{1-x^3}~?$$ I know wave ...
32 views

### Gauge Permitting c Magnetic Vector and Instant Electric Scalar Potentials?

The Lorenz gauge requires c propagation of both scalar and vector potentials. The Coulomb gauge requires instant "propagation" of these potentials but is stated in such a way as to permit c ...
81 views

### Significance of imaginary mass

Can real mass be thought of as producing a deformation in spacetime leading to a stable equilibrium (valley curve in gravitational potential energy) of the massive body, and imaginary mass as similar, ...
59 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 $n\geq 2$. ...
50 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 $V\left(\phi\right)$ ...
164 views

88 views

I have a system of two spheres, the first one is at a potential of $V_1 = 1 V$ and the second one is at a potential of $V_2 = 0 V$ The distance between them is $d$ and the radius are respectively $... 0answers 161 views ### Is hydrogen atom in a box solvable analytically? Schrödinger's equation for hydrogen atom in free space can be easily solved by switching to center of mass frame, introducing reduced mass and separating variables in the resulting 3D problem. But ... 0answers 85 views ### What is the physical meaning of the norm of the electromagnetic four-potential? In SI units this would be$\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? 0answers 47 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} \left\{-\frac{\... 0answers 495 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 ... 0answers 68 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 ... 0answers 149 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 ... 0answers 106 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 ... 0answers 771 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 ... 0answers 133 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 \... 0answers 12 views ### Electric octupole moment in cartesian coordinates I'm trying to calculate the symmetric traceless tensor for the octupole moment in cartesian coordinates... I have to deal with the electrostatic potential of the form: \Phi^{(4)}(\textbf{r})=\int d^{... 0answers 16 views ### Insulating cylinder with charge in a uniform electric field Suppose that we have a very long insulating cylinder of radius R on which we have placed some electrons such that it has a constant \sigma_0 charge per unit length. Assume that we then apply a ... 0answers 67 views ### Wavefunction of electron in 3D infinite well with non-zero potential Consider an electron moving in a potential V defined by$$V(x,y,z) = \left \{ \begin{array}{ll} \alpha(x^2 + y^2) & 0 \leq z \leq a \\ \infty & \text{otherwise} \end{array} \right. $$... 0answers 23 views ### Electric potential due to something What is the diffrence between "electric potential at some point due something" and "electric potential of something" ? 0answers 38 views ### Grounding system of conducting plates So, I always make mistakes on problems such as this (the grounding part), so I'm hoping someone could really explain to me how the process works . There are n large parallel plate conductors carrying ... 0answers 20 views ### Which is the form of Born-Mayer repulsion term? I have found in many textbooks different and unclear form of the Born-Mayer repulsion term. I write the interatomic potential as V(r)= -\frac{e^2}{r}+V_{BM} and for V_{BM} I expected something ... 0answers 58 views ### Finding \psi(0) using Schrodinger equation with potential U(x) = q\delta(x) I am having some trouble answering the following question in my "Advanced Quantum Mechanics" course: Using the integral equation:$$\psi(x) = Ae^{ikx} + Be^{-ikx} - \int_{-\infty}^{\infty}G^{\pm}(... 0answers 16 views ### Where is the zero electric potential energy point? Does the point of the electric potential energy of zero is defined by human or dominated by the indefinite integral of the electric force? 0answers 27 views ### Charge Magnitude Based on Isoline Spacing Suppose we have two positive charges of unknown magnitudes. We are given the isoline map (the equipotential lines) for the two-charge system. One has isolines more "squashed together" (more closely ... 0answers 31 views ### What is the relationship between potential energy and electrical potential? I actually always thought this was trivial, now I am not so sure. For a potential$\phi$the potential energy is$V=q\phi$where q is a test charge. Now I am thinking this may work differently in two ... 0answers 55 views ### What is the difference between length and velocity gauge when it comes to a dipole approximation? Lets say we have plane wave with$\vec E$perpendicular to$\vec k$. The dipole term will come from$\vec A\cdot \vec p$. Is the electric field longitudinal in the length gauge for the dipole ... 0answers 47 views ### How to find the minimum value of potential in QM? In MIT problem sets I followed a solution of an exercise which focuses on odd-parity energy eigenstates in finite square well. The point of problem is how to know or find the minimal value of ... 0answers 14 views ### Potential energy of a shell & point system Consider the system of a point particle with charge$q$and a spherical shell with uniform charge$Q$and radius$R$whose center is a distance$r > R$away from the point particle. I'm trying to ... 0answers 46 views ### Charged conducting wire ring and Greens function ρ(r) = q 2πa2 δ(r − a)δ(cos θ). If this is my charge distribution on a conducting wire ring. radius=a. I am attempting to show my electrostatic potential as an integral along the z-axis I started by ... 0answers 26 views ### Calculating potential differences: why integrate E- and not D-field? So here's my problem. I was thinking about the following. Let's say we have a parallel plate capacitor, filled completely with a dielectric medium. If we want to find the potential difference between ... 0answers 26 views ### Potential of a long cylinder from infinity I have a question about a long, effectively infinite, cylinder. The cylinder has a radius of$R_{1}$and charge density$\rho.$For$r>R_{1}$, the potential difference is$\Delta V_{ab} = \int_{a}^{...
Just wondering. The potential for the Higgs boson is given by: $$V(\varphi)=\lambda(\varphi^{2}-v^{2})^{2}$$ where $v≃$ 246 GeV is the vacuum expectation value required to explain mass in the ...
Say, we have a system of electrodes exhibiting symmetry around a certain axis. We know the explicit expression for the potential on the axis $\phi (z)$. We want to find the potential for any point in ...