2023-05-31T01:18:55Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/691322022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116A new estimate for the ground state energy of Schrdinger operatorsArai, A.open access410A new estimate for the ground state energy of Schrodinger operators on 2 L (Rn) (n 2: 1) is presented. As a corollary, it is shown that the ground state energy of the Schrodinger operator with a scalar potential V is more than the classical lower bound ess.inf xeRn V( x) if V is essentially bounded from below in a certain manner ( enhancement of the ground state energy due to quantization). As an application, it is proven that the ground state energy of the Hamiltonian of the hydrogen-like atom is enhanced under a class of perturbations given by scalar potentials (vanishing at infinity).Department of Mathematics, Hokkaido University1997-05-01engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83528http://hdl.handle.net/2115/6913210.14943/83528Hokkaido University Preprint Series in Mathematics382112https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69132/1/pre382.pdfapplication/pdf505.43 KB1997-05-01