Geodesic
Generalized convexity property for the energy of a~quantum-mechanical system
Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 3, pp. 432-438

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The energy $E$ of the lowest discrete level of a quantum-mechanical system is considered as a function of a parameter $\lambda$, that occurs linearly in the energy operator. An inequality that generalizes the well-known convexity property of the function $E(\lambda)$ is derived. The application of the generalized convexity property is illustrated by the example of the calculation of bounds for the total energies and the energies of the electron-nucleus interaction in the ground state for two-electron atoms. 
@article{TMF_1983_56_3_a9,
     author = {T. K. Rebane},
     title = {Generalized convexity property for the energy of a~quantum-mechanical system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {432--438},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a9/}
}
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T. K. Rebane. Generalized convexity property for the energy of a~quantum-mechanical system. Teoretičeskaâ i matematičeskaâ fizika, Tome 56 (1983) no. 3, pp. 432-438. http://geodesic.mathdoc.fr/item/TMF_1983_56_3_a9/