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22
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4answers
1k views

In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?

A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. Is there a one to one correspondence between the potential and its spectrum? If the ...
21
votes
4answers
6k views

Birds sitting on electric wires: potential difference between their feet

We have seen birds sitting on uninsulated electric wires of high voltage transmission lines overhead without getting harmed, because sitting on only one wire doesn't complete any circuit. But what ...
17
votes
6answers
1k views

Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
11
votes
8answers
9k views

What is the difference between electric potential, voltage and electromotive force?

This is a confused part ever since I started learning electricity. What is the difference between voltage and electromotive force (emf)? Both of them have the same SI unit, right? I would appreciate ...
10
votes
1answer
800 views

In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence?

The Lennard-Jones potential has the form: $$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$$ The (attractive) $r^{-6}$ term describes the ...
10
votes
1answer
1k views

3D Delta Potential Well

The 1D delta potential well $V(x) = -A\delta(x - a)$ always has exactly one bound state. The same is true for the 3D delta potential well $V(\vec{r}) = -A\delta(\vec{r}-\vec{a})$. I can show this for ...
9
votes
2answers
329 views

Motivation for Potentials

This is a hypothetical question about "pedagogy". Let's say I am trying to take someone who has just a very small amount of knowledge about Newtonian mechanics and convince them that the Lagrangian ...
8
votes
1answer
238 views

Anharmonic oscillators: why is $F=-k x-k' x^3$, with no quadratic terms?

The equation of motion of a general anharmonic oscillator includes a position-dependent force that can be expanded in a Taylor series as $$m\ddot{x}+2\mu\dot{x}+k_0+k_1x+k_2x^2+k_3x^3\ldots=F.$$ I ...
8
votes
5answers
479 views

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) = - ...
7
votes
6answers
224 views

Origins of many-particle interactions

The internal potential energy of an $N$ particle system is a general function of the coordinates of the particles: $U(r_1,...,r_N)$. In some approximations and expansions - e.g. virial expansion - it ...
7
votes
2answers
439 views

Infinite and Finite Square Wells

For the infinite square well in the first region, outside the well: $$\frac{-\hbar^2}{2m}\frac{d^2 \psi}{dx^2} + V(x) \psi (x) = E \psi (x),$$ where you set $V = 0$. Rearranging gives $$\frac{d^2 ...
7
votes
2answers
244 views

Is there a time delay during tunnelling?

A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process?
6
votes
4answers
563 views

Why can't we ascribe a (possibly velocity dependent) potential to a dissipative force?

Sorry if this is a silly question but I cant get my head around it.
6
votes
1answer
854 views

How to interpret the magnetic vector potential?

In electromagnetism, we can re-write the electric field in terms of the electric scalar potential, and the magnetic vector potential. That is: $E = -\nabla\phi - \frac{\partial A}{\partial t}$, ...
6
votes
2answers
1k views

How electric currents can flow between 2 points at the same potential?

According to Ohm's law, if there is a potential difference, $V$, across a resistor then there is a current, $I$, flowing through it. Since we assume that points along the connecting wire are at the ...
6
votes
2answers
406 views

Why do we like gauge potentials so much?

Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about ...
6
votes
2answers
154 views

Is there an equivalent of a scalar potential for torques?

For a given scalar potential $V$, it is known that the corresponding force field $\mathbf{F}$ can be computed from $$ \mathbf{F} = -\nabla V $$ Suppose a rigid body is placed inside this ...
5
votes
4answers
3k views

Why is electric potential scalar?

I can't conceptually visualize why it would be so. Say you have two point charges of equal charge and a point right in the middle of them. The potential of that charge, mathematically, is proportional ...
5
votes
2answers
614 views

Why does a capacitor discharge?

Suppose a charged capacitor (parallel plates), the negative and positive charges on two plates attract each other. Which force cause the negative charge carriers (electrons) move through the circuit ...
5
votes
1answer
118 views

Is there any good reason/argument/heuristic why one can approximate forces by approximating the potentials?

My question Is there any good reason/argument/heuristic why one can approximate forces by approximating the potentials? (As a concrete example, in Electrostatics.) Motivation for the question I am ...
5
votes
1answer
194 views

Kaluza-Klein Christoffel Symbols

I have a question regarding the connection coefficients as they pertain to the following paper: http://www.weylmann.com/kaluza.pdf . When I try to calculate the 4D Christoffel symbols from the 4D part ...
5
votes
4answers
951 views

How electron movement produces current,instead of having a slow drift speed

Just need a clarification here, how the current is produced due to the movement of electrons, in an external circuit,having a very slow drift speed. Normally in a battery there is high potential ...
5
votes
1answer
124 views

Apparent contradiction between calculations and intuition?

I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with. We have a potential step ...
5
votes
2answers
160 views

How does current flow in a irregularly shaped heterogeneous resistor?

The motivation for my question is understanding how electricity gets through your skin as opposed to running along it, and how the presence of things like water on the skin affect the relative ...
4
votes
4answers
4k views

Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get $$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty ...
4
votes
2answers
4k views

How can you have a negative voltage?

How can you have a negative voltage? I don't really understand the concept of negative voltage, how can it exist?
4
votes
2answers
1k views

Pn junction voltage drop?

This image from wikipedia, explains that there occurs a potential drop across a pn semiconductor junction, and an electric field confined to the depletion region. I already know the reason for the ...
4
votes
2answers
66 views

Definition of quantum anharmonicity

I have been reading research papers in mathematical physics for some months now, and I've seen the the term "anharmonic oscillator" quite frequently. At first I assumed that given a Schrodinger ...
4
votes
1answer
113 views

How do aspherical gravitational monopoles look like?

I was recently pointed by laboussoleestmonpays to a beautiful paper from some time ago, Aspherical gravitational monopoles. Alain Connes, Thibault Damour and Pierre Fayet. Nucl. Phys. B 490 no. ...
4
votes
1answer
209 views

Linear dependence of magnetic potential on current density

I'm a mathematician learning physics to provide some background for my mathematical work (especially pde's!). I have been reading through Jackson's Classical Electrodynamics (3rd edition), and I was ...
4
votes
1answer
130 views

Loopless voltage measurement

I think we are all very well familiarized with the classical voltmeter. Classical voltmeter has two conducting wires that bring two potentials into the box. In the box we have well controlled ...
4
votes
1answer
407 views

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 ...
4
votes
3answers
4k views

Force as gradient of scalar potential energy

My text book reads If a particle is acted upon by the forces which are conservative; that is, if the forces are derivable from a scalar potential energy function in manner $ F=-\nabla V $. I ...
4
votes
2answers
113 views

Argument for symmetry of potential

Consider the following electrostatic charge configuration of a spherically symmetric, perfect conductor with total charge $Q = 2q$, where $q > 0$. A point charge $q$ is placed at the position ...
4
votes
2answers
658 views

Where does the Pauli Repulsive Force come from that counteracts the attraction between atoms and ions? [duplicate]

I'm learning about such things as ionic and covalent bonds, and the reason given for the ionic bonds is electrostatic attraction. However, if that were true, then the two ions would accelerate toward ...
3
votes
2answers
519 views

Potential functions

Can someone please explain what a potential is? Example. velocity potential in ideal flows, acoustic potential (gradient of which gives the particle velocity in a sound wave). Whenever I see potential ...
3
votes
3answers
527 views

When Eigenfunctions/Wavefunctions are real?

When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real? What happens in 1D case like the finite ...
3
votes
2answers
5k views

How does electricity flow in conductor when potential difference is applied?

Electrons move from higher potential to lower potential. When a conductor is connected to battery, electron move from negative terminal to positive terminal. But the battery itself forms a Electric ...
3
votes
2answers
199 views

Strong Newton's third law of action and reaction: Mathematical Interpretation

According to the strong law of action and reaction for internal forces(Goldstein): "$F_{ij}=-F_{ji}$ and the forces lie along the direction joining the particles." Now consider the statement If ...
3
votes
2answers
10k views

Would you die if you put your hands on a powerline?

You know how birds perch on powerlines without getting electrocuted? What if by some chance that I find myself falling and I grab on one of them? Let's say both of my hands are on the same line, would ...
3
votes
3answers
82 views

Higher order derivatives - Equation of motion

One possible starting point to create a physical theory is the Lagrangian $L$. There we assume that the variation of the action $\delta S = \delta \int_{-\infty}^\infty dt \ L = 0$. In classical ...
3
votes
2answers
282 views

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 ...
3
votes
2answers
232 views

Alternative definitions of potential?

I hope this question is simple and can be quickly cleared up. In a 1D conservative dynamical system, I've always been taught that the potential function is the function $V(x)$ such that: ...
3
votes
2answers
431 views

Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be ...
3
votes
5answers
715 views

Infinite Wells and Delta Functions

In considering a delta potential barrier in an infinite well, I can just enforce continuity at the potential barrier-it doesn't have to go to zero. Why then does it need to go to zero at the walls of ...
3
votes
1answer
170 views

Is there any potential associated with magnetism

Can anybody please tell me if magnetism is a conservative force or if there is a field associated with it? How to reason? One thing I know is that the work done by a magnetic force is $0$.
3
votes
3answers
634 views

Can we have discontinuous wavefunctions in the Infinite Square well?

The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
3
votes
1answer
181 views

In $\textbf{f} = -\boldsymbol{\nabla} u$, what is $u$?

I know that force is the negative gradient of the potential: $$\textbf{f} = -\boldsymbol{\nabla} u$$ where force $\textbf{f}$ is a vector and $u$ is a scalar. This is a relatively soft question, ...
3
votes
1answer
42 views

What maintains constant voltage in a battery?

I know there's lots of questions that address similar situations, (Batteries connected in Parallel, Batteries and fields?, Naive Question About Batteries, and the oft-viewed I don't understand ...
3
votes
2answers
117 views

What is an “Interaction Hamiltonian”

I'm an undergraduate reading up on some quantum physics so that I can help out more in the lab that I'm working in this summer. In the book I'm reading (Shankar's "Principles of Quantum Mechanics") I ...