Using the coefficients demonstrate that is normalized

Reference no: EM13168796

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
<n|?>=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 ?.

Reference no: EM13168796

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