Pointwise bounds on eigenfunctions and wave packets in 𝑁-body quantum systems. II

Simon, Barry

doi:10.1090/S0002-9939-1974-99954-0

Pointwise bounds on eigenfunctions and wave packets in -body quantum systems. II

Author: Barry Simon
Journal: Proc. Amer. Math. Soc. 45 (1974), 454-456
MSC: Primary 35P99; Secondary 81.47
DOI: https://doi.org/10.1090/S0002-9939-1974-99954-0
Part I: Proc. Amer. Math. Soc. 42, no. 2 (1974), 395-401
MathSciNet review: 0417596
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Abstract: We provide a simple proof (and mild improvement) of Schnol's result that ${L^2}$ eigenfunctions of $- \Delta + V$ are $O(\exp ( - ar))$ for any whenever $V \to \infty$ as $r \to \infty$ .

[1] E. B. Davies, Properties of the Green's functions of operators, J. London Math. Soc. (to appear).
[2] J. M. Combes and L. Thomas, Asymptotic behavior of eigenfunctions for multiparticle Schrödinger operators, Comm. Math. Phys. 34 (1974), 251-270. MR 0391792 (52:12611)
[3] T. Kato, On the eigenfunctions of many-particle systems in quantum mechanics, Comm. Pure Appl. Math. 10 (1957), 151-177. MR 19, 501. MR 0088318 (19:501a)
[4] -, Perturbation theory for linear operators, Die Grundlehren der math. Wissenschaften, Band 132, Springer-Verlag, New York, 1966. MR 34 #3324. MR 0203473 (34:3324)
[5] E. Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572-615. MR 21 #5901. MR 0107176 (21:5901)
[6] A. O'Connor, Exponential decay of bound state wave functions, Comm. Math. Phys. 32 (1973), 319. MR 0336119 (49:895)
[7] M. Reed and B. Simon, Methods of modern mathematical physics. Vol. II, Academic Press, New York (to appear). MR 0493422 (58:12430a)
[8] T. Regge and V. de Alfaro, Potential scattering, North-Holland, Amsterdam; Interscience, New York, 1965. MR 32 #8724. MR 0191316 (32:8724)
[9] J. E. Šnol', On the behavior of the eigenfunctions of Schrödinger's equation, Mat. Sb. 46 (88) (1957), 273-286; erratum, 259. (Russian) MR 23 #A2618.
[10] B. Simon, Pointwise bounds on eigenfunctions and wave packets in -body quantum systems. I, Proc. Amer. Math. Soc. 42 (1974), 395-401. MR 0417596 (54:5646)
[11] -, Quantum mechanics for Hamiltonians defined on quadratic forms, Princeton Univ. Press, Princeton, N. J., 1971.