A particle is in the state:
$|\psi\rangle = 0.5 |1\rangle - 0.6 |2\rangle + a |3\rangle$
where the energies are $E_1 = 1$ eV, $E_2 = 3$ eV, and $E_3 = 6$ eV.

(a) Determine a possible value for $a$
(b) Find $< E >$ (note, we don't do this in the current iteration of PHYS 212)
(c) The particle's energy is measured to be 6 eV. What is the state of the particle immediately after this measurement?