Time evolution of a two-state system

[Milsomonk]

Homework Statement

Hey guys,
I have a question that asks;
Assume an Electron Nuetrino (U1) is produced at t = 0. Find the state U(t) for later times t > 0.

To give some context the question is based on a two state system where U1 = Collumn vector (sin(theta) cos(theta)) and U2 = Collumn vector (-sin(theta) cos(theta)).

Homework Equations

The Attempt at a Solution

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I get that its asking me to essentially write the system with the time dependance, and I can't simply bolt the time dependence exponential on the end because U1/U2 are not generally eigenstates of the hamiltonian. So I need to expand U(t=0) in terms of energy eigenstates and then I can include the time dependant exponential for t>0.
Im just not sure how to do this, since I know its in the state U1 at t=0 what's to expand? any advice would be appreciated :)

 

[Orodruin]

A good start would be to express U1 in the mass eigenstates.

 

[Milsomonk]

Hmmm, we havn't covered that, we havn't looked in any detail at the specific case of nuetrino oscillations. I think he was just hoping to make us think about simple two state systems rather than nuetrino oscillations themselves.

 

[Orodruin]

Well, there is nothing specifically peculiar for the case of neutrino oscillations. The same procedure will be applicable to any two level system.

Are you saying you have not seen how to write an arbitrary vector as a linear combination of a set of basis vectors?

 

[Milsomonk]

No sorry, it was the mass eitrnstates I haven't seen before.