Which of the following is a possible eigen value of the operator \(\hat{\mathrm{L}}_{\mathrm{x}}^{2}+3 \hat{\mathrm{L}}_{\mathrm{y}}^{2}+\sqrt{3}\left(\hat{\mathrm{L}}_{\mathrm{x}} \hat{\mathrm{L}}_{y}+\hat{\mathrm{L}}_{\mathrm{y}} \hat{\mathrm{L}}_{x}\right)\) ? (\(\hat{\mathrm{L}}_{\mathrm{x}}\), \(\hat{\mathrm{L}}_{\mathrm{y}}\) are components of the orbital angular momentum operator)
1
\(\hbar^{2}\)
2
\(4 \hbar^{2}\)
3
\(\sqrt{3} \hbar^{2}\)
4
\(3 \hbar^{2}\)