Geodesic
On~the~Schr\"{o}dinger equation with a~random potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 6 (1971) no. 3, pp. 415-424

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A study is made of the ergodic properties of various quantities connected with a Schrödinger equation with a random potential. For the case when the potential is a metrically transitive (ergodic) random field with realizations that are bounded below it is shown that these quantities tend to nonrandom limits with probability 1 when the volume in which the equation is considered tends to infinity. It is shown that these limiting values are independent of the boundary conditions. 
@article{TMF_1971_6_3_a9,
     author = {L. A. Pastur},
     title = {On~the~Schr\"{o}dinger equation with a~random potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {415--424},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_6_3_a9/}
}
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L. A. Pastur. On~the~Schr\"{o}dinger equation with a~random potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 6 (1971) no. 3, pp. 415-424. http://geodesic.mathdoc.fr/item/TMF_1971_6_3_a9/