Wave Packet in Quantum Cosmology and Definition of Semiclassical Time

We consider a quantum cosmology with a massless background scalar field $\text{pb}$ and adopt a wave packet as the wave function. This wave packet is a superposition of the WKB form wave functions, each of which has a definite momentum of the scalar field $\text{pb}$. In this model it is shown that to trace the formalism of the WKB time is seriously difficult without introducing a complex value for a time. We define a semiclassical real time variable $\text{tp}$ from the phase of the wave packet and calculate it explicitly. We find that, when a quantum matter field $\text{pq}$ is coupled to the system, an approximate Schr"odinger equation for $\text{pq}$ holds with respect to $\text{tp}$ in a region where the size $a$ of the universe is large and $\mathrm{\mid }\text{pb}\mathrm{\mid }$ is small.