Unitary transformations depending on a small parameter
F. Casas, J. Oteo, and J. Ros. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences468 (2139):
We formulate a unitary perturbation theory for quantum mechanics inspired by the Lie-Deprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples.