Understanding Interference Between Spin States

[metroplex021]

I'm reading about decoherence, and I've found I don't understand the most basic thing. Interference between terms in a superposition is only possible, I thought, if the two terms are not orthogonal. But then how can up and down spin states (with respect to some direction) interfere with one another?!

thanks!

 

[Bill_K]

It would help to hear more about the context, but I think you have to make a distinction between interference and coherence. If two states |ψ1> and |ψ2> are orthogonal they can't directly interfere with each other. Nevertheless they may be in a coherent superposition α|ψ1> + β|ψ2>, meaning there remains the possibility of interference between them following a transition to another state |φ>.

 

[metroplex021]

Thank you... I am fundamentally confused! Could you maybe give an example of such a transition that could lead to inference between orthogonal states?

 

[Bill_K]

What I'm suggesting is that when you ask for the transition probability to a state |φ>, if the phases of |ψ1> and |ψ2> have been randomized you'll just get two terms, αα*<φ|ψ1><ψ1|φ> + ββ*<φ|ψ2><ψ2|φ>. But if the states are coherent you'll get as well the cross terms αβ*<φ|ψ2><ψ1|φ> + α*β<φ|ψ1><ψ2|φ>. I may be off base, but I think this relates to what you're asking.