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Regarding to the asymptotic solution of quantum harmonic oscillator

You need to be careful on defining the asymptotics. From the equation: $$ u''+\left(\epsilon-x^2-\frac{l(l+1)}{x^2}\right)u = 0 $$ you want to know the behaviour of $u$ at infinity. The issue is that ...
LPZ's user avatar
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Rescaling time in differential equations

It is the non-dimensionalization of the last two differential equations. Assuming $g$ as the acceleration due to gravity ($\text{m}/\text{s}^2$) and $l$ as the length (m), $\sqrt{l/g}$ has the ...
Pustam Raut's user avatar
3 votes
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Rescaling time in differential equations

It's an usual procedure in deriving non-dimensional equations, from the dimensional ones: angles have no physical dimensions, they wanted a "scaled" (non-dimensional) time as well. You just ...
basics's user avatar
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Why we take only the real part of a solution as the actual motion?

to solve this ode $$\ddot\eta+\omega^2\eta=0\quad , \omega^2=\frac VT$$ you make this ansatz $$\eta(t)=(a+b\,i)\,e^{i\,\omega\,t}+(a-b\,i)\,e^{-i\,\omega\,t}\quad,a,b\in Re\tag 1$$ from the Initial ...
Eli's user avatar
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Why we take only the real part of a solution as the actual motion?

You are correct, the imaginary part is also a solution. And you could even go further: any combination of the real part and the imaginary part of a complex solution can be used. If the complex ...
Jos Bergervoet's user avatar
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Why we take only the real part of a solution as the actual motion?

I think the reason for the sentence "It is understood of course that it is the real part of (6.11) that is to correspond to the actual motion" Is that $\eta_i$ represents (likely) the ...
lcv's user avatar
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Static solution to an implicitly dynamic problem - heat equation

Some interpretations that may be useful: The transient conductive heat equation says that if the temperature is decreasing in some region $\left(\frac{dT}{dt}<0\right)$, then the net curvature of ...
Chemomechanics's user avatar
1 vote

Static solution to an implicitly dynamic problem - heat equation

For the 3D space, generically, I have: $ u=f(x,y,z,t) $ As pointed out by @Jon when I set: $ \frac{\partial u}{\partial t}=-1 $ $ \frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2} ...
Megidd's user avatar
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Green's function solution in 2D for the potential of solenoids in the Lorenz gauge

There are some wrong assumptions here. Firstly, your integral (1) actually does give answer (2), how did you find the opposite conclusion?! Also, the fact that the Green function diverges at infinity ...
Jos Bergervoet's user avatar

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