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## Homework Statement

We have a linear combination of eigenstates of observable A [tex]\Phi_+[/tex] and [tex]\Phi_-[/tex] with eigenstates a and -a. The expected value of the energy for both states is 0, while [tex](\Phi_+,H\Phi_-)=E[/tex], with E real. Calculate the expected value of A for eigenstates [tex]\Phi_+[/tex] and [tex]\Phi_-[/tex] over time.

## Homework Equations

I guess

[tex](\Phi_+,H\Phi_+)=(\Phi_-,H\Phi_-)=0[/tex]

[tex](\Phi_+,H\Phi_-)=E[/tex]

[tex]\varphi=C_+\Phi_++C_-\Phi_-[/tex]

## The Attempt at a Solution

I guess that for the given equations I have to obtain <H>

[tex]<H>=\varphi^*H\varphi=(C_+\Phi_++C_-\Phi_-)^*H(C_+\Phi_++C_-\Phi_-)=C_+^*C_+(\Phi_+^*,H\Phi_+)+C_-^*C_-(\Phi_-^*,H\Phi_-)+C_+^*C_-(\Phi_+^*,H\Phi_-)+C_-^*C_+(\Phi_-^*,H\Phi_+)[/tex]

Then I assume C's and [tex]\Phi[/tex]'s are real so

[tex]<H>=2C_+C_-E[/tex]

Now I have to compute this

[tex]<A>=(\varphi^*,A\varphi)[/tex]

How <H> plugs into the calculation of <A>?