Ground state hydrogen parallel to the double slit experiment?

[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.

 

[tom.stoer]

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!

 

[doghouseriley]

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')

 

[tom.stoer]

... the electron has/can have zero spin?

No!

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

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

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.

[tex]\langle nlms|\hat{S}_z|nlms\rangle = 0[/tex]

 

[PJC01]

I would like to clarify that the double slit experiment is a thought experiment and does not involve actual electrons going through the slits. It is used as a conceptual tool to understand the wave-particle duality of particles at the quantum level. Therefore, the parallel between the ground state of hydrogen and the double slit experiment is not applicable.

The ground state of hydrogen refers to the lowest energy state of the electron in a hydrogen atom, where it is most likely to be found. This is a well-defined state and does not involve any superposition or interference. The electron cannot be in both spin up and spin down states at the same time, as this would violate the laws of quantum mechanics.

In the double slit experiment, the interference pattern is observed when the electron's wave function passes through both slits simultaneously. This is a result of the uncertainty principle, which states that we cannot know the exact position and momentum of a particle at the same time. Therefore, it is not possible to apply the concept of superposition to the ground state of hydrogen, as this state is well-defined and does not involve any uncertainty.

Furthermore, the concept of superposition and observation in the double slit experiment is specific to the quantum world and does not have a direct parallel in the macroscopic world. In the macroscopic world, we can observe objects without significantly affecting their state, whereas in the quantum world, the act of observation can change the state of the particle.

In conclusion, while the double slit experiment is a fascinating concept that helps us understand the behavior of particles at the quantum level, it is not directly applicable to the ground state of hydrogen. The ground state of hydrogen is a well-defined state and does not involve any superposition or interference.