In quantum system, one usually computes the eigenvalue problem of the Schroedinger operator to obtain the energy band structure. When eigenvalues become degenerate, wave packet that travels along one energy band could jump to other energy bands, and the transition coefficients are hard to compute. We solve this problem using the standard Wigner transform approach. This technique, however, usually only works away from the degenerate point. We resolve it by taking the off-diagonal elements into account, and successfully recover the transition coefficients. In particular my talk is based on two examples, the electron dynamics near band touchings in a crystal, and the surface-hopping problem around conical crossings in a molecule when the Born-Oppenheimer approximation breaks down.