With the expression for the ground-state wavefunction, lets keep going and construct the wavefunction of the first excited state, 1(x), of the harmonic oscillator. Recall

With the expression for the ground-state wavefunction, let’s keep going and construct the wavefunction of the first excited state, ψ1(x), of the harmonic oscillator.

Recall that the relationship between the ground state and the first excited state from Eq. (6.44) is

|v) = a*|yo). (6.76)