Waveguides and radiation

Consider a state described by $\Psi(x, t) = \psi_2(x, t) + \psi_4(x, t)$, where $\psi_2(x, t)$ and $\psi_4(x, t)$ are respectively the second and fourth normalized harmonic oscillator wave functions and $\omega$ is the angular frequency of the harmonic oscillator. The wave function $\Psi(x, t = 0)$ will be orthogonal to $\Psi(x, t)$ at time $t$ equal to:

Options:

• (A) $\frac{\pi}{2\omega}$
• (B) $\frac{\pi}{\omega}$
• (C) $\frac{2\pi}{\omega}$
• (D) $\frac{\pi}{4\omega}$