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 behaviour of eigenfunctions for multiparticle Schrödinger operators, Comm. Math. Phys. 34 (1973), 251–270. MR 0391792
[3] Tosio Kato, On the eigenfunctions of many-particle systems in quantum mechanics, Comm. Pure Appl. Math. 10 (1957), 151–177. MR 0088318, https://doi.org/10.1002/cpa.3160100201
[4] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
[5] Edward Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572–615. MR 0107176, https://doi.org/10.2307/1970331
[6] A. J. O’Connor, Exponential decay of bound state wave functions, Comm. Math. Phys. 32 (1973), 319–340. MR 0336119
[7] M. Rid and B. Saĭmon, \cyr Metody sovremennoĭ matematicheskoĭ fiziki. 1: Funktsional′nyĭ analiz., Izdat. “Mir”, Moscow, 1977 (Russian). Translated from the English by A. K. Pogrebkov and V. N. Suško; With a preface by N. N. Bogoljubov; Edited by M. K. Polivanov. MR 0493422
[8] V. de Alfaro and T. Regge, Potential scattering, North-Holland Publishing Co., Amsterdam; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1965. MR 0191316
[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] Barry Simon, Pointwise bounds on eigenfunctions and wave packets in 𝑁-body quantum systems. I, II, Proc. Amer. Math. Soc. 42 (1974), 395–401: ibid. 45 (1974), 454–456. MR 0417596, https://doi.org/10.1090/S0002-9939-1974-99954-0
[11] -, Quantum mechanics for Hamiltonians defined on quadratic forms, Princeton Univ. Press, Princeton, N. J., 1971.