%0 Journal Article %T Energy Optimal Interpolation in Quantum Evolution %A Xiao Ge %A Zhan Xu %J Physics %D 2008 %I arXiv %X We introduce the concept of interpolation in quantum evolution and present a general framework to find the energy optimal Hamiltonian for a quantum system evolving among a given set of middle states using variational and geometric methods. A few special cases are carefully studied. The quantum brachistochrone problem is proved as a special case. %U http://arxiv.org/abs/0809.3183v1