Ground state hydrogen parallel to the double slit experiment?

AI Thread Summary
The discussion explores the parallels between the double slit experiment and the ground state of hydrogen, particularly regarding electron spin. It highlights that while an electron can exist in a superposition of spin states, it does not imply that the electron has zero spin. Instead, the electron is in a state with a zero expectation value for spin, meaning it can be in both spin up and spin down states simultaneously without being observed. The conclusion is that the electron does not have a specific spin eigenvalue but exists in a superposition of states. Overall, the conversation clarifies the nature of quantum states in relation to observation and measurement.
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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