[QUE/QFT-05003] QFT-PROBLEM

Prove that the free particle solutions \(f_q(x)\) obey the orthononality relations \begin{eqnarray} i \int d^3x f_q^*(x) \overleftrightarrow{\partial}_0 f_p(x) = 2\omega_q\delta(\vec{q}-\vec{p}).\nonumber \end{eqnarray} and find the value of \( \int d^3x f_q(x) \overleftrightarrow{\partial}_0 f_p(x)\).