# Another Two Questions (fluids And Quantics)

1. Dec 28, 2004

### Raparicio

Dear Friends,

Two more questions that I could not find the resolution. If anyone knows where is resolved, or could give a little help, I will be so much agreed!!!

One is about fluids mechanics: imagine one ball, in a fluid composed by much little balls. At much velocity, this big ball could adquire mass from this entorn, and be bigger. What's de velocity of equilibrium that makes that the ball has not acceleration. Imagine that the ball is little at principle, but it creates much big ball derivate of the material arround it. Another example could be a ball of snow running, at much velocity, much bigger...

Another question is about biot-savart law, in fluids mechanics. I dont understand the meaning of the strength... is this the circulation?

And another question is about demonstration of schrödinger equation by the formulae of continuity. I don't know how to do it.

I desire all of you a very good day.

R. Aparicio.

2. Dec 28, 2004

### dextercioby

Who says/how did u deduce that the sphere must have an equilibrium??What are the forces that act on the sphere??Similarly,who said that a rolling snowball could be in equilibrium (i'm assuming it rolls down a mountain covered with snow)???Again,what forces act on it??

I've never heard of contributions of Jean Baptist Biot,Félix Savart & Pierre Simon (marquis de) Laplace in fluid dynamics as to come up with an identical law to the one they found in classical magnetostatics...Can u write the formula??Maybe i'll figure out what it means...

It's the other way around actually.Schroedinger's equation is a postulate in the QM in the Schroedinger picture and the Dirac (traditional,vectors+operators) formulation.That's why it makes sense to go from:
$$\frac{\partial\Psi(\vec{r},t)}{\partial t}=\frac{1}{i\hbar}\frac{\hat{p}^{2}}{2m} \Psi(\vec{r},t)$$
,where
$$\hat{p}=-i\hbar \nabla \hat{1}$$
,to
$$\frac{\partial\rho(\vec{r},t)}{\partial t}+\nabla\cdot \vec{j}(\vec{r},t)=0$$
,where $\rho(\vec{r},t);\vec{j}(\vec{r},t)$ are the localization probability density and the probability current density,respectively.

Daniel.

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