What is the expectation value of ĤHO for the state Ψvib in terms of ħω? (Refer to the image for the problem) The general vibrational state of a diatomic molecule can be exactly described by expandingits wave function in the set of orthonormal harmonic oscillator (HO) wave functions. Thelatter are definedAHOW,HO = E,Ho y,HO with the set of associated eigenvalues E,H0 = ħw (n + %)The vibrational state of a particular diatomic molecule is prepared in a state described bythe normalized wavefunctionWvib = 1/(2)1/2 w, HO + 1/ (3)/2 W̟HO + 1/(6)1/2 w,HOWhat is the expectation value of AHO for the state Wvib in terms of ħw?

Given: The vibrational state of a particular diatomic molecule described by the normalized…

The general vibrational state of a diatomic molecule can be exactly described by expanding its wave function in the set of orthonormal harmonic oscillator (HO) wave functions. The latter are defined AHoWnH0 = E,Ho w,HO with the set of associated eigenvalues E,HO = ħw (n + %) The vibrational state of a particular diatomic molecule is prepared in a state described by the normalized wavefunction Wvib = 1/(2)1/2 w, HO + 1/ (3)/2 W̟HO + 1/(6)/2 w,HO What is the expectation value of AHO for the state Wyib in terms of ħw?

The general vibrational state of a diatomic molecule can be exactly described by expanding its wave function in the set of orthonormal harmonic oscillator (HO) wave functions. The latter are defined AHoWnH0 = E,Ho w,HO with the set of associated eigenvalues E,HO = ħw (n + %) The vibrational state of a particular diatomic molecule is prepared in a state described by the normalized wavefunction Wvib = 1/(2)1/2 w, HO + 1/ (3)/2 W̟HO + 1/(6)/2 w,HO What is the expectation value of AHO for the state Wyib in terms of ħw?