# Interpretation Schrödinger's formulae

1. May 8, 2005

### Raparicio

Dear Friends,

Does anybodi knows the meaning, or anything related to the term:

$$\Psi \nabla \Psi^*$$

or

$$\Psi \nabla \Psi^* - \Psi^* \nabla \Psi$$

Is the representation of something in the reality?

Best reggards.

2. May 8, 2005

### Galileo

If you have a particle having a wavefunction $\psi(\vec r, t)$, then:

$$\vec J(\vec r,t)=\frac{\hbar}{2mi}(\psi^* \nabla \psi-\psi\nabla \psi^*)$$

is the so-called probability current. It represents the flow of probability density, like electrical current is the flow of charge density.

3. May 8, 2005

### Raparicio

Spinor?

Thanks, Galileo, but I'm trying to "imagine" what is, for example, one of the 2 terms:

$$\psi^* \nabla \psi$$

Has it any meaning? Is a rotor of the nabla operator?

4. May 8, 2005

### dextercioby

Nope,it's just the ~ to the integral nucleus of the momentum operator.

Daniel.

5. May 8, 2005

### rune

Sorry if this is really basic, i'm no quantum guru yet :tongue:, but could you say that the (classical) velocity is in the direction where $$\vec J$$ has global max at a given $$t$$? Is it possible somehow to calculate $$\vec v$$ from $$\vec J$$?

Last edited: May 8, 2005
6. May 9, 2005

### dextercioby

"(Classical) velocity" has nothing to do with the probability current density...

Daniel.

7. May 9, 2005

### Raparicio

empirical

empirical experiments verify this formulae is ok?

8. May 9, 2005

### dextercioby

Which formulae...?We can't measure $\vec{j}\left(\vec{r},t\right)$,but only probabilities.

Daniel.

9. May 9, 2005

### Raparicio

Chr

Daniel,

I mean that if exists any experiment or example in real word that confirms that formula or some of its components. For example, if the probability to find a particle in some place or time has this formula...

10. May 9, 2005

### dextercioby

I'm not an experimentalist and never will be,but i can assure that this simple part of QM has been fully checked and confirmed.We can't measure certain abstract things.Since QM is a probabilistic theory,all we can do is statistics.

Daniel.

11. May 9, 2005

tks Daniel.