Spinor Spreading: Relation between \psi and \chi

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Discussion Overview

The discussion revolves around the relationship between the spatial factor \(\psi\) and the spinor \(\chi\) in the context of particle description, particularly focusing on the concept of spreading and visualization of spinors. The scope includes theoretical and conceptual aspects of quantum mechanics.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that a full description of a particle is represented by the product \(\psi \chi\).
  • One participant asserts that a spinor does not spread, suggesting that the visualization of a spinor should not involve spreading concepts.
  • Another participant suggests visualizing the spinor "cloud" as a conical surface made of up vectors, questioning if this representation is correct.
  • There is a discussion about the implications of applying a magnetic field, with references to Larmor precession and its effects on the density of the spinor representation.
  • One participant humorously questions the terminology used regarding Larmor precession, indicating a playful tone in the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the nature of spinors and their visualization, with no consensus reached on the correct representation or understanding of spinors in relation to spatial factors.

Contextual Notes

There are unresolved assumptions regarding the definitions and properties of spinors and their relation to spatial factors, as well as the implications of applying magnetic fields.

intervoxel
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Since a full description of a particle is the product \psi \chi, what's the relation between the spreading of the spatial factor \psi and of its spinor \chi?
 
Last edited:
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intervoxel said:
Since a full description of a particle is the product \psi \chi, what's the relation between the spreading of the spatial factor \psi and of its spinor \chi?

Hi intervoxel! :smile:

A spinor doesn't spread. :wink:
 
Ok, tiny-tim, a spinor doesn't spread. Thank you. :)

So, I suppose, we can visualize the spinor "cloud" as a conical surface (s=1/2, up state, say) made of up vectors with length hbar/2 centered around an axis in a certain direction in space so that its projection on that direction alone always returns the value hbar/2, while for others directions we might obtain any value, positive or negative. Is this picture correct?

In the case when we apply a magnetic field in that direction the Lamour precession means that the cone is denser (greater probability) around a vector precessing at the Lamour frequency. Is it?
 
Last edited:
… on the road to Morocco …

intervoxel said:
So, I suppose, we can visualize the spinor "cloud" as a conical surface (s=1/2, up state, say) made of up vectors with length hbar/2 centered around an axis in a certain direction in space so that its projection on that direction alone always returns the value hbar/2, while for others directions we might obtain any value, positive or negative. Is this picture correct?

Hi intervoxel! :smile:

Any "cloud" that you see in diagrams of electron distributions has nothing to do with the spinor.

There is nothing conical about a spinor.

The spinor just defines the direction of spin …

if you want to visualise a spinor as a volume, then use a sphere, rotating about the axis defined by the spinor. :smile:
In the case when we apply a magnetic field in that direction the Lamour precession means that the cone is denser (greater probability) around a vector precessing at the Lamour frequency. Is it?

Is that the Dorothy Lamour precession? :wink:

She gets around, doesn't she?
 

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