Positive perturbations of self-adjoint Schrödinger operators. (English) Zbl 0571.35021
Given a Schrödinger operator \(T_ 0=-\Delta +q_ 0\) which is bounded from below and essentially selfadjoint on \(C_ 0^{\infty}\), it is shown that \(T=T_ 0+q\) for \(q\geq 0\) is also essentially selfadjoint, if T is relatively bounded. The result is applied to approximations of positive elements in the domain of T.
Reviewer: H.Siedentop
MSC:
| 35J10 | Schrödinger operator, Schrödinger equation |
| 47B25 | Linear symmetric and selfadjoint operators (unbounded) |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
References:
| [1] | Cycon, J. Operator Theory 6 pp 75– (1981) |
| [2] | Cycon, Internal J. Math. 5 pp 545– (1982) |
| [3] | Cycon, Proc. Roy. Soc. Edinburgh Sect. A 86 pp 165– (1980) · Zbl 0462.35019 · doi:10.1017/S0308210500012099 |
| [4] | Brézis, J. Operator Theory 1 pp 287– (1979) |
| [5] | DOI: 10.1007/BF02028443 · Zbl 0353.35032 · doi:10.1007/BF02028443 |
| [6] | Reed, Modern Methods of Mathematical Physics, II (1975) |
| [7] | DOI: 10.1007/BF01174567 · Zbl 0409.35026 · doi:10.1007/BF01174567 |
| [8] | Kato, Proc. Roy. Soc. Edinburgh Sect. A. 96 pp 323– · Zbl 0555.35025 · doi:10.1017/S0308210500025440 |
| [9] | Kato, Pertubation theory for linear operators (1966) |
| [10] | DOI: 10.1007/BF01113402 · Zbl 0228.47010 · doi:10.1007/BF01113402 |
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