the wave-function & the distinct states of electrons

[ether]

Greetings to all

 

May I please enquire about how the wave-function predicts the position of electrons? What I am most concerned about is how it deals with the defined states that electrons occupy. I am sure you are aware of the simplified explanations describing an ‘electron cloud’ around the nucleus, so how does this take into account the distinct states they occupy?

 

Many thanks

[swansont]

The "cloud" is a probability distribution for each distinct state. That describes the position as well as you can.

[ether]

In simplified terms, can I assume the states of the electrons (compared with each other) are comparable to different dimensions, in other words if we have two electrons in the first electron orbital, the distance of the wave-functions cloud from the nucleus (for both electrons) will be the same, but we know they will ‘never’ cross paths, hence they occupy (from their own perspectives) different dimensions.

 

Please excuse the simplification of my terminology.

[swansont]

In simplified terms, can I assume the states of the electrons (compared with each other) are comparable to different dimensions, in other words if we have two electrons in the first electron orbital, the distance of the wave-functions cloud from the nucleus (for both electrons) will be the same, but we know they will ‘never’ cross paths, hence they occupy (from their own perspectives) different dimensions.

 

Please excuse the simplification of my terminology.

 

 

No, not really. "Crossing paths" is something that doesn't have much meaning in this context.

[ether]

"No, not really."

 

?

 

"Crossing paths" is something that doesn't have much meaning in this context.

 

thats exactly why i used the example of them occuppying different dimensions!

 

 

 

[Severian]

In simplified terms, can I assume the states of the electrons (compared with each other) are comparable to different dimensions, in other words if we have two electrons in the first electron orbital, the distance of the wave-functions cloud from the nucleus (for both electrons) will be the same, but we know they will ‘never’ cross paths, hence they occupy (from their own perspectives) different dimensions.

 

No. There are two electrons in the first orbital because they have different spin. They are allowed to occupy exactly the same state as long as they differ in some other quantum number, in this case spin. You could think of spin as being another dimension is you like (since it is another degree of freedom) but you need to keep in mind that it is discrete, and there is no concept of distance (no metric).

[swansont]

"No, not really."

 

?

 

"Crossing paths" is something that doesn't have much meaning in this context.

 

thats exactly why i used the example of them occuppying different dimensions!

 

 

 

 

 

"Crossing paths" is a classical, spatial concept, and isn't pertinent here, so you threw me a little by using it. If you are wondering what is different between two electrons in e.g Helium, given that they have basically the same spatial wave function, then Severian has given the answer; spin is an orthogonal degree of freedom.

[Norman Albers]

Electrons are the identifiable manifestations of whatever you want to call the available vacuum. So is all the rest of this, namely, available resonances.

[Norman Albers]

I do not mean to be flip here. I am involved in exciting discussions taking off from my realizations of the electron field itself, as well as gravitation studies, of the states of the vacuum polarizability in these different but not totally distinct regimes. Severian, I like that statement of spin being another degree of freedom. It is the intrinsic particle characteristic and THE NEWS is that the different levels of angular momentum interact. As a senior in college this struck me like a freight train.