A certain harmonic oscillator wavefunction ?(x) is NOT an eigenfunction of the Hamiltonian operator. Rather it is a superposition of three harmonic oscillator eigenstates. Given that
??1*?dt=<1|?>=1/sqrt(2)
<2|?>=<3|?>=1/2
=0 if n is NOT 1, 2, or 3
a. Write as a superposition of 3 eigenstates, indicating the numerical value of each coefficient.
b. Using the coefficients, demonstrate that is normalized.
c. Find the expectation value of energy (in units of h) in state ?.