# Tag Info

1 vote
Accepted

### 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 ...
• 12.2k

### 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 ...
Accepted

### 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 ...
• 8,671

### 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 ...
• 12.3k

### 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 ...
• 2,422
Accepted

### 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 ...
• 2,364
Accepted

### 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 ...
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} ...
• 123