Abstract
A method recently introduced for obtaining rigorous lower bounds to the true quantum-mechanical expectation value of a positive operator F >or= 0 is here extended and strengthened. The new formula always improves the previous result, but requires the more difficult integrals of FH and H2. As a numerical illustration, lower bounds are calculated for various powers of r1 and r12 in the normal helium atom. Using, particularly, the quantum-mechanical virial theorem and an improved lower bound for the overlap integral , it is shown that rigorous lower bounds accurate to 5-30% can be obtained even from the simple screened hydrogenic approximation, and the nuclear diamagnetic shielding is given correct to 1%.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
