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.
Cite
@article{arxiv.0809.3183,
title = {Energy Optimal Interpolation in Quantum Evolution},
author = {Xiao Ge and Zhan Xu},
journal= {arXiv preprint arXiv:0809.3183},
year = {2008}
}