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## Homework Statement

A spin system with only 2 possible states

H = ([tex]^{E1}_{0}[/tex] [tex]^{0}_{E2}[/tex])

with eigenstates

[tex]\vec{\varphi_{1}}[/tex] = ([tex]^{1}_{0}[/tex]) and [tex]\vec{\varphi_{2}}[/tex] = ([tex]^{0}_{1}[/tex])

and eigenvalues E1 and E2.

Verify this & how do these eigenstates evolve in time?

## Homework Equations

I'm even not sure how to start...

Maybe someone could help me out, I'd come up with an attempt if I'd know how. Thanks!