Ground state hydrogen parallel to the double slit experiment?

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Discussion Overview

The discussion explores the analogy between the double slit experiment and the ground state of hydrogen, particularly focusing on the behavior of the electron's spin states. Participants examine whether the wave functions of the electron's spin can superimpose in a manner similar to the interference pattern observed in the double slit experiment.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants propose that, similar to the double slit experiment, the electron in the ground state of hydrogen can exist in a superposition of spin states (spin up and spin down) as long as it is not observed.
  • One participant asserts that the electron can indeed be in both spin states at once, suggesting that this leads to a zero spin state.
  • Another participant challenges the idea of the electron having zero spin, clarifying that while the electron does not have a specific spin eigenvalue, it exists in a superposition that results in a zero expectation value for spin.
  • A mathematical representation of the hydrogen atom's state is provided to illustrate the concept of superposition in relation to the electron's spin.

Areas of Agreement / Disagreement

Participants express differing views on whether the electron can be said to have zero spin, with some supporting the idea of superposition leading to a zero spin state, while others refute this claim, emphasizing the distinction between having a specific spin value and the expectation value being zero.

Contextual Notes

The discussion involves assumptions about the nature of quantum states and the interpretation of superposition, which may not be universally agreed upon. The mathematical representation provided is contingent on specific definitions and interpretations of quantum mechanics.

doghouseriley
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In the double slit experiment the electron can go through either slit. As long as it is not observed there is an interference pattern as the two possibilities superimpose. The common conclusion to this is that the electron goes through both slits.

Is there a parallel with the ground state of hydrogen? One electron has two states it can be in - spin up/spin down. Does this mean the wave functions for both situations superimpose and it is in both states at once as long as it is not observed (giving a spin of zero!)

I'm sure the answer to this is an abrupt and sharp 'No' but I was wondering why not.
 
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doghouseriley said:
Does this mean the wave functions for both situations superimpose and it is in both states at once as long as it is not observed?
Yes!
 
tom.stoer said:
Yes!

Oh right! So is it pushing it to say the electron has/can have zero spin?

Answers need not be restricted to the quantum states of 'thumbs up' ('yes') or 'thumbs down' ('no') :biggrin:
 
doghouseriley said:
... the electron has/can have zero spin?
No!

Consider for simplicity a state of the hydrogen atom of the form

|nlms\rangle = |nlm\rangle \frac{1}{\sqrt{2}}\left(|s=+1/2\rangle - |s=-1/2\rangle\right)

So the electron does not have zero spin, but it is in a state with zero expectation value. As there is no reason why the electron should have one specific spin eigenvalue, it is in a superposition of both states.

\langle nlms|\hat{S}_z|nlms\rangle = 0
 
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