[QUE/QFT-05003]

Prove that the free particle solutions of Klein Gordon equation \(f_q(x)\), given by
\[ f_q(x) = \frac{1}{\sqrt{(2\pi)^3}} e^{-iqx},\]  obey the orthononality relations \[ \begin{eqnarray}   i \int d^3x f_q^*{x} \{\partial_0 f_p(x)\} - \{\partial _0 f_q(x)\} f_p^*(x) = 2\omega_q\delta(\vec{q}-\vec{p}). \end{eqnarray} \] and find the value of \( \int d^3x \big[f_q(x) (f_q(x) \{\partial_0 f_p(x)\} - \{\partial _0 f_q(x)\} f_p(x))\big]\)