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 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) = - \frac{\alpha}...
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Can I determine the potential term in the Schrödinger equation based on the eigenvalues? [duplicate]

Let's imagine I knew a certain system could be described by a one-dimensional Schroedinger equation. I know the mass/momentum term, but not the shape of the potential. Further for some reason I know ...
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Demonstration of the existence of a scalar potential for a conservatice force

Mathematically a vector field, $\vec{F}$, is conservative if: $$\oint_{\gamma} (\vec{F}.d\vec{l})=0$$ Physically, the integral is the same as the work done by a force $\vec{F}$ on a body in a closed ...
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Perturbation theory for a particle in a weak potential

I have a basic question about quantum mechanics, maybe it has a basic answer. Take a free particle in a quartic potential, $L=\frac{1}{2}\dot{x}^2-\lambda x^4$ This is massless $\phi^4$ theory in 0+...
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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): $\mathbf F_\mathrm {ij}=-\mathbf F_\mathrm{ji}$ and the forces lie along the direction joining the particles. ...
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Gravitational potential in GR

Why in GR does the $g_{\mu\nu}$ describe potential?
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How does instant charging of one plate affect the potential of the other plate of a floating capacitor?

If I have an uncharged floating capacitor and I instantaneously connect one plate to some potential, then that plate will acquire some charge. In practice, the other floating plate will ...
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How can direction of electric field due to a moving charge be from the present position of charge?

According to Maxwell's Equations, the electromagnetic waves in vacuum travel at the speed of light $c$. While solving Maxwell's equations using Lorenz gauge conditions (or basically evaluating scalar ...
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QM: Finite Potential Square Well Solved without Symmetry Assumption

as the title suggests I'm trying to figure out the solution of the finite potential well, without using the odd/even symmetry of the potential. $$ V(x) = \begin{cases} 0 & \text{otherwise} \...
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Energies and numbers of bound states in finite potential well

Hello I understand how to approach finite potential well (I learned a lot in my other topic here). However i am disturbed by equation which describes number of states $N$ for a finite potential well ( ...
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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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What is the difference between the potential energy and the energy of a test charge due to the electric field?

We are taking the electrostatic course in physics class, and I was wondering about some things related to potential, potential energy, and electric field. Imagine two identical particles with opposite ...
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When QM particle in a box is in the first excited state, will it be ever found at the middle point, ie. at the nodal point?

Reading the wikipedia article about the particle in the box, there is this image: Animations from B to F show wave function of a particle in a box starting from ground state up to excited states. The ...
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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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What is the physical reason for why gravitational potential (or electrical potential) due to two masses at a point can simply be added algebraically?

The simple explanation that textbooks and the internet say is that "gravitional potential is a scalar quantity hence can be added algebraically". However, I'm not sure if it is that simple. Take for ...
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Facing a paradox: Earnshaw's theorem in one dimension

Consider a one-dimensional situation on a straight line (say, $x$-axis). Let a charge of magnitude $q$ be located at $x=x_0$, the potential satisfies the Poisson's equation $$\frac{d^2V}{dx^2}=-\frac{\...
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Wave function with a delta potential

I have a particle and a potential $V(x)=\frac{\hbar^2}{2m}k\delta(x)$. Where $\delta (x)$ is the Delta function, and I am interested in the solutions of the stationary Schroedinger equation. If $\...
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Why can we pick the divergence of the vector potential? [duplicate]

I'm aware that the vector and scalar potential in E&M can be modified using a function $\lambda(t)$ in the following way: $$\mathbf{A}' = \mathbf{A} + \nabla\lambda,\;\; \textrm{ and } \;\;\Phi' =...
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Plotting $\psi$ for finite square well potential

Lets say we have a finite square potential well like below: This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
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Solving a time independent Schrödinger equation with a given potential

I'm trying to rework this old homework problem, and I am having problems arriving at the same solution on the answer sheet: Let $$V(x)=\begin{cases}\infty &\text{ if } x < 0\\ \alpha\delta(x-...
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Lagrangian of Non-Relativistic Charged Particle in a Magnetic Field

I'm trying to derive the Lagrangian for a non-relativistic charged particle under the influence of a magnetic potential. I'm assuming that $F=-\textrm{grad}(V)$ and so by the Lorentz force we have $-\...
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Direction of Potential Gradient & Electric field

Potential gradient is the negative of the electric field: $dV=-\vec{E}\cdot \operatorname{d}\!\vec{r}$ Does the negative sign mean that the direction of potential gradient $\operatorname{d}\!V\!/\!...
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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?
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Is potential difference or potential used in defining capacitance?

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 ...
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How does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?

So we are looking at central potentials in QM; The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$. We have; $$\hat{H}=-\...
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Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]

A particle of mass m moves on the x-axis under the influence of the potential $$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$ Can anyone help me, using Schrödinger's equation in one dimension that the energy ...