%0 Journal Article %1 QUA:QUA22924 %A Marmorino, M. G. %A Cassella, Kayleigh %D 2011 %I Wiley Subscription Services, Inc., A Wiley Company %J International Journal of Quantum Chemistry %K analysis expectation inequality mathematics mechanics physics quantum value %N 14 %P 3588--3596 %R 10.1002/qua.22924 %T Bounds to electronic expectation values for atomic and molecular systems %U http://dx.doi.org/10.1002/qua.22924 %V 111 %X A generalization of a method to calculate lower bounds to expectation values of non-negative observables is presented. We consider bounds to three electronic expectation values <r2>, <r>, and <r−1> in the helium atom as an example. For both <r2> and <r>, we are able to calculate improved lower bounds. The lower bound to <r−1> does not improve, but we are able to calculate an upper bound which is much closer to the expectation value than the lower bound. Although our generalization allows for improved bounds and/or upper bounds, these bounds to general observables are much less precise than energy bounds and even the expectation values calculated from variational wave functions.

@article{QUA:QUA22924, abstract = {A generalization of a method to calculate lower bounds to expectation values of non-negative observables is presented. We consider bounds to three electronic expectation values <r2>, <r>, and <r−1> in the helium atom as an example. For both <r2> and <r>, we are able to calculate improved lower bounds. The lower bound to <r−1> does not improve, but we are able to calculate an upper bound which is much closer to the expectation value than the lower bound. Although our generalization allows for improved bounds and/or upper bounds, these bounds to general observables are much less precise than energy bounds and even the expectation values calculated from variational wave functions.}, added-at = {2011-09-15T00:44:19.000+0200}, author = {Marmorino, M. G. and Cassella, Kayleigh}, biburl = {https://www.bibsonomy.org/bibtex/28c8b9b90b121e941041b15448d38eaaa/drmatusek}, doi = {10.1002/qua.22924}, interhash = {d618cdaa8d36f7074dd1a41d7f52ae36}, intrahash = {8c8b9b90b121e941041b15448d38eaaa}, issn = {1097-461X}, journal = {International Journal of Quantum Chemistry}, keywords = {analysis expectation inequality mathematics mechanics physics quantum value}, month = {November}, number = 14, pages = {3588--3596}, publisher = {Wiley Subscription Services, Inc., A Wiley Company}, timestamp = {2012-12-06T03:30:46.000+0100}, title = {Bounds to electronic expectation values for atomic and molecular systems}, url = {http://dx.doi.org/10.1002/qua.22924}, volume = 111, year = 2011 }