# Ground state hydrogen parallel to the double slit experiment?

1. May 30, 2010

### doghouseriley

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.

2. May 30, 2010

### tom.stoer

Yes!

3. May 30, 2010

### doghouseriley

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')

4. May 30, 2010

### tom.stoer

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.

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

Last edited: May 30, 2010