# 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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### Field inside a wire?

This answer gives a great explanation of why the field inside a wire connected to a battery must be equal at all points: Why doesn't the electric field inside a wire in a circuit fall off with ...
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### Increasing a potential causes increase in energy levels

Suppose a potential $V(x)$, and suppose a bound particle so the allowed energy levels are discrete. Suppose a second potential $\widetilde{V}(x)$ such that $\widetilde{V}(x) \geq V(x)$ for all $x$ (...
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### Why doesn't $σ_xσ_p$ change with the width of the well in the infinite square well problem (intuition)?

I calculated that the product of the uncertainty in position $\sigma_x$ for the ground state of an infinite square well of width $L$ with the uncertainty in the momentum $\sigma_p$ for the same state, ...
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### Time-Dependent Potentials in Quantum Mechanics

A potential that depends on time is usually solved using the time dependent perturbation theory in standard undergraduate textbooks in quantum mechanics. The reason usually mentioned is that time ...
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### Why is voltage described as potential energy per charge?

Voltage is often called an electromotive force since it causes a flow of charge. However, it is described in terms of Joules per Coulomb or Potential Energy per Charge. Question: How does the ...
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### Can potential be velocity dependent?

In the lagrangian solution for the equation of motion, there's a seemingly out of place $$\frac{\mathrm{d} }{\mathrm{d} t}\frac{\partial V}{\partial \dot{q_j}}$$ term. Potential energy is usually a ...
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### What does electric potential mean in a circuit?

As we know that electric potential at a point is defined as a work done by me to carry unit charge from infinity to that point. How can I use this definition in an electric circuit that contains a ...
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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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### Imaginary potential and stationary wavefunction

If the external potential $V$ in the time-dependent Schroedinger equation doesn't depend on time, then we can separate the wavefunction as spatial part and time part. $$\Psi(x,t)=\psi(x) \theta(t)$$...
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### Why does the first radial excitation of a particle in a 2D annulus $a<r<b$, for $b\gg a$ lie between the second and third azimuthal excitations?

Consider the quantum mechanics of a massive particle confined by infinite potential walls to a 2D annulus $a<r<b$, for which the Hamiltonian's eigenfunctions obey the stationary Schrödinger ...
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### Does the potential energy related to a particle determines its rest mass?

Would it be possible to determine the rest mass of a particle by computing the potential energy related to the presence (existence) of the particle, if this potential energy could be determined ...
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### 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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### 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 ...
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### Wave function of a particle in a gravitational field

Suppose we have a particle with mass $m$ and energy $E$ in a gravitational field $V(z)=-mgz$. How can I find the wave function $\psi(z)$? It should have an integral form on $dp$. Any help would be ...
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### Particle in a box plus step (ground state)

I am trying to come up with a QM problem that: Can be solved analytically Contains a potential that is a sum of some analytically solvable potential and another contribution: $V'=V_0 + V$ Is then ...
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### George Green's derivation of Poisson's equation

I was reading George Green's An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, and I got confused on one step in his derivation of Poisson's Equation. ...
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### Initial condition for Fourier transformed Schrödinger equation

I asked in this thread Time-dependet Schrödinger equation how to solve the Time-dependent Schrödinger equation. One of JamalS' recommendations was the Fourier transform, which is why I want to quote ...
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### Does the electric field inside a circuit cause a potential drop with distance?

We know that when the system reaches steady-state(current does not change with time),the electric filed inside the circuit is constant. In many textbooks and lectures,professors make a graph like this ...
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### Work done in an equipotential surface is zero?

An equipotential surface is one in which all the points are at the same electric potential. If a charge is to be moved between any two points (say from point A to point B) on an equipotential surface, ...
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### How is the Schrödinger equation solved for time varying curved potential barriers?

How would the Schrödinger equation be solved for curved barriers which change as a function of time, e.g., a paraboloid potential barrier with maximum height, $V$ changing with time into a Hyperboloid ...
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### How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential is ...
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### If the electric field is the gradient of the potential, then can we say that whenever potential is zero, the electric field is zero?

For example, in a dipole, at the center of the two charges making up the dipole, the potential is zero but the electric field is non-zero. But if $E = -\operatorname{grad}V$, then why is $E$ not zero? ...
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### Deriving Konopinski's Operational Definitions of Scalar and Vector Potential

In "What the electromagnetic vector potential describes", E. J. Konopinski asserts: Operational definitions of Φ, A should now be expected to stem from the equation of motion (2) when it is ...
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### 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 take ...
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### How to derive the expression for the electric field in terms of the potential?

How can I derive that $$\vec{E}=-\vec{\nabla}\phi-\frac{\partial \vec{A}}{\partial t}$$ where $\phi$ is the scalar potential and $\vec{A}$ the vector potential?
In my textbook I came across the capacitance of a certain body (i.e. a sphere, not two different spheres as in a spherical capacitor) and in it the formula, $$Q = CV$$ where $V$ is the potential of ...