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Taylor expansion for a double well/perturbed infinite square well

I'm trying to estimate the ground state energy for a perturbed infinite square well directly. The potential is piecewise constant $$V(x)=\begin{cases}&\infty, \qquad x<-a/2\\ &0 \qquad -a/2&...
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2answers
36 views

Why should the spherically asymmetric part of the effective potential be small in the central field approximation?

In the central field approximation, each electron is supposed to move in an effective or average potential contributed by its attractive interaction with the nucleus and repulsive interaction with the ...
-2
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1answer
106 views

Can anyone explain the harmonic oscillator (in context to quantum mechanics) 2.3 (Griffiths) using Taylor series?

At the end he concludes $V(x) = V''(x_0)(x-x_0)^2$. How does he get to know that the rest are $0$? How does he conclude $V''(x_0) = k$. Please try to explain in easy ways and tough vocabulary. I don't ...
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1answer
55 views

Strong force gets weaker at small distances yet approximated by -1/r potential

My particle physics textbook (by Martin and Shaw) has confused me, it states in ch.7 that the strong force gets weaker at small distances, and that it can be approximated by $V(r) = -\frac{4 \alpha_s}{...
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1answer
157 views

Gauss' law: Infinitely long cylinder approximation

Why approximating a cylinder as infinitely long works when $R << L$? Where $R$ is the radius and $L$ is the length of the cylinder. I was able to prove for a line of charges when r << L (...
3
votes
1answer
634 views

Understanding multipole expansion in classical electrodynamics

I am trying to better understand what the multipole expansion means from a phyiscal point of view. Although mathematically, one may say it is just another form of a series expansion, in this case, the ...
3
votes
1answer
190 views

Limit example in Zangwill “Modern Electrodynamics”

Zangwill shows that the potential of a finite line segment going from $-L$ to $L$ on the $z$-axis with constant line charge density $\lambda$ is: $$\phi(z,\rho) = \frac{\lambda}{4\pi\epsilon_0}\ln\...
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1answer
89 views

On the ansatzes of potentials in quantum mechanics [closed]

Here are the list of quantum-mechanical potentials. My question is how did scientists physically model these potentials, what were the parameters they consider before mathematically constructing a ...
3
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1answer
1k views

Why is the Taylor expansion of the gravitational potential cut off after first term?

In this answer to a question on this site, the gravitational potential of the Earth is expanded as $$U(r) \approx U(r_0) + \left.\frac {dU(r)}{dr}\right|_{r=r_0}(r-r_0),$$ keeping only the linear term....
3
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1answer
3k views

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 ...