Geodesic
Schr\"odinger-type operator over $p$-adic number field
Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 323-333

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The spectral properties of a Schrödinger-type $p$-adic operator are studied. The self-adjointness of the minimal operator is proved. The completeness of the eigenvectors, the asymptotic behavior of the eigenvalues, and the position of the essential spectrum are considered. 
@article{TMF_1991_86_3_a0,
     author = {A. N. Kochubei},
     title = {Schr\"odinger-type operator over $p$-adic number field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--333},
     publisher = {mathdoc},
     volume = {86},
     number = {3},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_86_3_a0/}
}
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A. N. Kochubei. Schr\"odinger-type operator over $p$-adic number field. Teoretičeskaâ i matematičeskaâ fizika, Tome 86 (1991) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/TMF_1991_86_3_a0/