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_{z}= h/2 [1 0 // 0 -1] for up spin.So can we say that the energy of the electron in this state is h/2 ?

(since S

_{z}|up> = h/2 |up>)

Now we consider a Hamiltonian H = [1 0 // 0 -1] which has eigen values +1, -1 and the respective states are

(1 0) and (0 1).

If we see the Schrodinger's equation it gives :

H |1 0 > = 1 * |1 0> which says energy of | 1 0 > is = 1.

We take same hamiltonian, same state, but once we are getting energy eigen value 1/2 ,next time we are getting 1.

Where I am getting it wrong ?