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A new proof of the Mourre estimate. (English) Zbl 0514.35025

MSC:
35J10 Schrödinger operator, Schrödinger equation
35B35 Stability in context of PDEs
Citations:
Zbl 0477.35069
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[1] S. Agmon, Lectures on exponential decay of solutions of second order elliptic equations , Bounds on eigenfunctions of \(N\)-body Schrödinger operators, to be published. · Zbl 0503.35001
[2] V. Enss, A note on Hunziker’s theorem , Comm. Math. Phys. 52 (1977), no. 3, 233-238.
[3] R. Froese and I. Herbst, Exponential bounds and absence of positive eigenvalues for \(N\)-body Schrödinger operators , to appear in Commun. Math. Phys. · Zbl 0509.35061
[4] H. Kalf, The quantum mechanical virial theorem and the absence of positive energy bound states of Schrödinger operators , Israel J. Math. 20 (1975), 57-69. · Zbl 0302.35072
[5] E. Mourre, Absence of singular continuous spectrum for certain selfadjoint operators , Comm. Math. Phys. 78 (1980/81), no. 3, 391-408. · Zbl 0489.47010
[6] P. Perry, I. M. Sigal, and B. Simon, Spectral analysis of \(N\)-body Schrödinger operators , Ann. of Math. (2) 114 (1981), no. 3, 519-567. JSTOR: · Zbl 0477.35069
[7] I. M. Sigal, Geometric methods in the quantum many-body problem. Nonexistence of very negative ions , Comm. Math. Phys. 85 (1982), no. 2, 309-324. · Zbl 0503.47041
[8] B. Simon, Geometric methods in multiparticle quantum systems , Comm. Math. Phys. 55 (1977), no. 3, 259-274. · Zbl 0413.47008
[9] B. Simon, personal communication. · Zbl 1077.41007
[10] J. Weidmann, The virial theorem and its application to the spectral theory of Schrödinger operators , Bull. Amer. Math. Soc. 73 (1967), 452-456. · Zbl 0156.23304
[11] G. M. Zhislin, Discussion of the spectrum of the Schrödinger operator for systems of many particles , Tr. Mosk. Mat. Obs. 9 (1960), 81-128. · Zbl 0121.10004
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