no. 4
Pointwise bounds on the asymptotics of spherically averaged L 2 -solutions of one-body Schrödinger equations
Annales de l'I.H.P. Physique théorique, Tome 42 (1985) no. 4, pp. 341-361. 
@article{AIHPA_1985__42_4_341_0,
     author = {Hoffmann-Ostenhof, M. and Hoffmann-Ostenhof, T. and Swetina, J\"org},
     title = {Pointwise bounds on the asymptotics of spherically averaged $L^2$-solutions of one-body {Schr\"odinger} equations},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {341--361},
     publisher = {Gauthier-Villars},
     volume = {42},
     number = {4},
     year = {1985},
     mrnumber = {801233},
     zbl = {0595.35033},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1985__42_4_341_0/}
}
TY  - JOUR
AU  - Hoffmann-Ostenhof, M.
AU  - Hoffmann-Ostenhof, T.
AU  - Swetina, Jörg
TI  - Pointwise bounds on the asymptotics of spherically averaged $L^2$-solutions of one-body Schrödinger equations
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1985
SP  - 341
EP  - 361
VL  - 42
IS  - 4
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1985__42_4_341_0/
LA  - en
ID  - AIHPA_1985__42_4_341_0
ER  - 
%0 Journal Article
%A Hoffmann-Ostenhof, M.
%A Hoffmann-Ostenhof, T.
%A Swetina, Jörg
%T Pointwise bounds on the asymptotics of spherically averaged $L^2$-solutions of one-body Schrödinger equations
%J Annales de l'I.H.P. Physique théorique
%D 1985
%P 341-361
%V 42
%N 4
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1985__42_4_341_0/
%G en
%F AIHPA_1985__42_4_341_0
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Swetina, Jörg. Pointwise bounds on the asymptotics of spherically averaged $L^2$-solutions of one-body Schrödinger equations. Annales de l'I.H.P. Physique théorique, Tome 42 (1985) no. 4, pp. 341-361. http://www.numdam.org/item/AIHPA_1985__42_4_341_0/

[1] S. Agmon, Lectures on exponential decay of solutions of second order elliptic equations. Bounds on eigenfunctions of N-body Schrödinger operators, Mathematical Notes, Princeton University Press, Princeton N. J., 1982. | MR | Zbl

[2] B. Simon, Schrödinger semigroups, Bull. Am. Math. Soc., t. 7, 1982, p. 447-526. | MR | Zbl

[3] R. Carmona, B. Simon, Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems V: Lower bounds and path integrals, Commun. Math. Phys., t. 80, 1981, p. 59-98. | MR | Zbl

[4] R. Froese and I. Herbst, Exponential bounds on eigenfunctions and absence of positive eigenvalues for N-body Schrödinger operators, Commun. Math. Phys., t. 87, 1982, p. 429-447. | MR | Zbl

[5] R. Froese, I. Herbst, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, L2-exponential lower bounds to solutions of the Schrödinger equations, Commun. Math. Phys., t. 87, 1982, p. 265-286. | MR | Zbl

[6] C. Bardos and M. Merigot, Asymptotic decay of solutions of a second order elliptic equation in an unbounded domain. Application to the spectral properties of a Hamiltonian, Proc. Roy. Soc. Edinburgh Sect., t. A 76, 1977, p. 323-344. | MR | Zbl

[7] R. Froese, I. Herbst, Exponential lower bounds to solutions of the Schrödinger equation: lower bounds for the spherical average, Commun. Math. Phys., t. 92, 1983, p. 71-80. | MR | Zbl

[8] B. Simon, Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems III, Trans. Amer. Math. Soc., t. 208, 1975, p. 317-329. | MR | Zbl

[9] T. Hoffmann-Ostenhof, A comparison theorem for differential inequalities with applications in quantum mechanics, J. Phys., t. A 13, 1980, p. 417-424. | MR | Zbl

[10] E.B. Davies, JWKB and related bounds on Schrödinger eigenfunctions, Bull. London Math. Soc., t. 14, 1982, p. 273-284. | MR | Zbl

[11] R. Ahlrichs, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, J. Morgan, Bounds on the decay of electron densities with screening, Phys. Rev., t. A 23, 1981, p. 2106-2116. | MR

[12] R. Froese, I. Herbst, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, L2-lower bounds to solutions of one-body Schrödinger equations, Proc. Roy. Soc. Edinburgh, t. 95 A, 1983, p. 25-38. | MR | Zbl

[13] W.O. Amrein, A.M. Berthier, V. Georgescu, Lower bounds for zero energy eigen-functions of Schrödinger operators. Helv. Phys. Acta, t. 57, 1984, p. 301-306. | MR | Zbl

[14] M. Reed, B. Simon, Methods of modern mathematical physics IV. Analysis of operators, Academic Press, New York, 1978. | MR | Zbl

[15] W.O. Amrein, A.M. Berthier, V. Georgescu, Lp-inequalities for the Laplacian and unique continuation, Ann. Inst. Fourier, t. 31, 1981, p. 153-168. | Numdam | MR | Zbl

[16] L. Hörmander, Uniqueness theorems for second order elliptic differential equations, Commun. P. D. E., t. 8, 1983, p. 21-63. | MR | Zbl

[17] M. Aizenman, B. Simon, Brownian motion and Harnack's inequality for Schrödinger operators, Comm. Pure, Appl. Math., t. 35, 1982, p. 209-271. | MR | Zbl

[18] M. Abramowitz, I.A. Stegun, Handbook of mathematical functions, Dover, New York, 1968.

[19] H.D. Block, A class of inequalities, Proc. Amer. Soc., t. 8, 1957, p. 844-851. | MR | Zbl

[20] M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, Anzeiger der Österr. Akad. d. Wiss., t. 8, 1976, p. 91-95, | Zbl

[21] T. Kato, Perturbation theory for linear operators, Springer New York, 1976, 2nd ed. | MR | Zbl

[22] C.B. Morrey, Multiple integrals in the calculus of variations, Springer New York, 1966. | MR | Zbl

[23] M. Reed, B. Simon, Methods of mathematical physics II, Fourier analysis, selfadjointness, Academic Press, New York, 1975. | Zbl

[24] M. Hoffman-Ostenhof, T. Hoffmann-Ostenhof, Schrödinger inequalities and asymptotic behaviour of the one density of atoms and molecules, Phys. Rev., t. A 16, 1977, p. 1782-1785. | MR