This chapter describes the second part of the quantum/classical mixed approach, computation of vibrational spectra from the vibrational Hamiltonian. There are two methods to carry out this computation. One is time-averaging approximation (TAA) that is computationally less expensive but more approximate. The other is wave function propagation (WFP) that is more expensive but more rigorous. In either method, the vibrational Hamiltonian is diagonalized to obtain eigenvalues and eigenvectors that allow for computing the vibrational spectra with a clear correspondence to the trajectories of molecular dynamics simulations. Although we first learn WFP in this chapter, readers unfamiliar with the time-dependent Schrödinger equation and time correlation function may skip WFP and jump to TAA where only the time-independent Schrödinger equation is needed. Although TAA is more approximate, it performs as excellently as WFP in terms of comparison between calculations and experiments.