# 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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### Can we solve the particle in an infinite well in QM using creation and annihilation operators?

The particle in an infinite potential well in QM is usually solved by easily solving Schrodinger differential equation. On the other hand particle in the harmonic oscillator oscillator potential can ...
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### Sphere half-submerged on a dielectric

This is a classic problem in electrostatics with a twist, so I thought it could be useful for others here. I did have a problem with the integration at the end, but on general I think the idea can ...
164 views

### $D$-dimensional Schrodinger's equation with a Dirac delta potential

I know that for $D\geq 2$, there is no bound state for a Dirac potential $V=-\alpha \delta(\textbf{x})$ unless we use an ultraviolet cutoff $k_{max}=1/a$. I showed this by solving the Schrodinger's ...
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### Why is the spin-orbit interaction for a nucleus so much more important than the spin-orbit interaction in atomic physics?

In atomic physics, the spin-orbit is a small correction between 1/1000 and 10ppm, so fairly small. In contrast, in nuclear physics the inclusion of the spin-orbit interaction is necessary to reproduce ...
229 views

### Understanding conformal mapping in electrostatics

I'm trying to understand the use of conformal mapping to solve problems in electrostatics. To better understand the idea, I'm trying to learn how to solve this example (but you can propose any other ...
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### Common potential in Capacitors

If two isolated charged capacitors (of different capacitance) are connected in parallel to each other they acquire a common potential. But suppose if i connect positive plate of one capacitor to ...
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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 \...
117 views

### What is a good analogy for electric potential?

When the electrical field was defined I could totally relate to $\vec{E}$ being like $\vec{g}$ in mechanics. But for the electric potential I don't know what would be equivalent analogy. Any ...
101 views

### How to derive the simplest 1D Superpotential Hamiltonian?

In the superpotential wiki article there are definitions of two supersymmetric operators: $$Q_1=\frac{1}{2}\left[(p-iW)b+(p+iW)b^\dagger\right] \\ Q_2=\frac{i}{2}\left[(p-iW)b-(p+iW)b^\dagger\right]$$...
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### Method of image charges for a point charge and a non-grounded conducting plane

I know how to solve Laplace's equation for a point charge in front of a grounded conducting infinite plane. But I want to know what happens (both physics and math) when the infinite conducting plane ...
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### Is there something wrong in my book's derivation of work done on charge?

For finding potential at a point due to a +ve charge $(q)$, we find work done to move a unit +ve charge $(q_o)$ from infinity to that point in the presence of +ve charge $(q)$ Since both charges ...
309 views

### Accelerated ion beam current

If an electron gun creates a $10\space mA$ electron beam and each electron collides with a gas atom and creates an ion through impact ionization, can the ions then be accelerated with a separate ...
101 views

### Conservation of momentum in statistical physics in presence of a potential

Imagine a number of particles, all confined in a parabolic potential. The particles initially have a random velocity and are let free to bounce off each other (say, it's rigid spheres). Does ...
201 views

### Does a Static E-field Increase the Gauge Invariant Vector Potential Without Bound?

The gauge invariant formulation of Maxwell's Laws (7.13): Indicates that the transverse electric field is the time derivative of the transverse vector potential. This gauge invariant vector ...
61 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 ...
123 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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### Power series solution for a shifted spherical harmonic oscillator

I'm trying to solve the Schrodinger equation for a radial Harmonic oscillator whos equilibrium point has been shifted away from the origin, i.e. $V(r) = V_0(r-1)^2$. The standard approach is to make ...
39 views

### What exactly do the zero-modes of the instanton mean?

I am studying instantons in quantum mechanics. My question is regarding the the zero mode of the fluctuation determinant that we get because the solution for the instanton breaks time translation ...
39 views

### Gravitational Potential Derivation

The definition of Gravitational Potential at a point is the work done per unit mass in moving it from infinity to that point. However the work is positive and if you perform the integral you get a ...
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### Does the potential $V(φ)$ of a scalar field decrease with the expansion of space?
If a scalar field (eg. inflaton field) starts with a high potential. Does the potential $V(φ)$ of the scalar field decrease with the expansion of space? If it doesn’t decrease, would it mean that ...