PT Journal
AU Casas, F
   Oteo, JA
   Ros, J
TI Unitary transformations depending on a small parameter
SO Proceedings of the Royal Society A
JI Proc. R. Soc. A
PY 2012
BP 685
EP 700
VL 468
IS 2139
DI 10.1098/rspa.2011.0388
LA English
DE perturbation theory; quantum mechanics; unitary transformation; Magnus expansion
AB 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.
ER