Unitary transformations depending on a small parameter
, , and .
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468 (2139): 685-700 (March 2012)

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.
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