Repeat exercise 3 for the third state (second excited state) \(|3angle\) of the harmonic oscillator, namely, for \(\psi_{a}(x)=y^{2} e^{-a y^{2}}\).

Data From Exercise 3:-

Use the practical variational method for the same harmonic oscillator ground state energy, with trial wave function \(\psi_{a}(x)=e^{-a y^{2}}\).