Geodesic
Conditions for the self-adjointness of the Schrodinger operator
Matematičeskie zametki, Tome 8 (1970) no. 6, pp. 741-751

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Sufficient conditions are derived for the self-adjointness of the Schrödinger operator in the whole of space and in bounded regions, without supplementary boundary conditions and without any requirements concerning the existence of a spherically symmetric minorant of the potential satisfying the Titchmarsh–Sears conditions. 
@article{MZM_1970_8_6_a6,
     author = {F. S. Rofe-Beketov},
     title = {Conditions for the self-adjointness of the {Schrodinger} operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {741--751},
     publisher = {mathdoc},
     volume = {8},
     number = {6},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_6_a6/}
}
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F. S. Rofe-Beketov. Conditions for the self-adjointness of the Schrodinger operator. Matematičeskie zametki, Tome 8 (1970) no. 6, pp. 741-751. http://geodesic.mathdoc.fr/item/MZM_1970_8_6_a6/