The absence of eigenvalues for certain operators with partially periodic coefficients. (English. Russian original) Zbl 1497.35402
St. Petersbg. Math. J. 33, No. 5, 867-878 (2022); translation from Algebra Anal. 33, No. 5, 176-192 (2021).
Summary: The absence of eigenvalues is proved for the Schrödinger operator \(-\Delta + V(x,y)\) in the Euclidean space whose potential is periodic in some variables and decays in the remaining variables faster than power 1. A similar result for the Maxwell operator is established.
MSC:
| 35Q40 | PDEs in connection with quantum mechanics |
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35P10 | Completeness of eigenfunctions and eigenfunction expansions in context of PDEs |
| 78A30 | Electro- and magnetostatics |
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