Using the trial function
\(\psi(x)=\left\{\begin{array}{cc} A\left(a^2-x^2\right), & -a
the ground state energy of a one-dimensional harmonic oscillator is
1
ħω
2
\(\sqrt{\frac{5}{14}} \hbar \omega\)
3
\(\frac{1}{2} \hbar \omega\)
4
\(\sqrt{\frac{5}{7}} \hbar \omega\)