%0 Journal Article %1 casas12012unitary %A Casas, F. %A Oteo, J. A. %A Ros, J. %D 2012 %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %K consistent mechanics perturbation physics quantum size theory %N 2139 %P 685-700 %R 10.1098/rspa.2011.0388 %T Unitary transformations depending on a small parameter %U http://rspa.royalsocietypublishing.org/cgi/content/abstract/468/2139/685 %V 468 %X 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.

@article{casas12012unitary, abstract = {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. }, added-at = {2012-01-27T17:03:36.000+0100}, author = {Casas, F. and Oteo, J. A. and Ros, J.}, biburl = {https://www.bibsonomy.org/bibtex/2a17c78940e2719f5e6f989cf542e6ca6/drmatusek}, doi = {10.1098/rspa.2011.0388}, interhash = {73544d4eee2fba4aebb4b1c83d4e206f}, intrahash = {a17c78940e2719f5e6f989cf542e6ca6}, journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, keywords = {consistent mechanics perturbation physics quantum size theory}, month = {March}, number = {2139 }, pages = {685-700}, timestamp = {2013-04-17T13:06:18.000+0200}, title = {Unitary transformations depending on a small parameter}, url = {http://rspa.royalsocietypublishing.org/cgi/content/abstract/468/2139/685}, volume = 468, year = 2012 }