journal article
Feb 01, 1979
Born series for (2 cluster) ? (2 cluster) scattering of two, three, and four particle Schr�dinger operators
Communications in Mathematical Physics
Vol. 66
No. 1
pp. 77-94
·
Springer Science and Business Media LLC
Topics
No keywords indexed for this article. Browse by subject →
References
24
[1]
Aaron, R., Klein, A.: Convergence of the Born expansion. J. Math. Phys.1, 131?138 (1960)
10.1063/1.1703643
[2]
Agmon, S.: Spectral properties of Schrödinger operators and scattering theory. Ann. Scuola Norm. Sup. Pisa Ser. IV,2, 151?218 (1975)
[3]
Balslev, E.: Absence of positive eigenvalues of Schrödinger operators. Arch. Rat. Mech. Anal.59, 343?357 (1975)
10.1007/bf00250424
[4]
Balslev, E.: Decomposition of many-body Schrödinger operators. Commun. Math. Phys.52, 127?246 (1977)
10.1007/bf01625780
[5]
Faddeev L.D.: Mathematical aspects of the three-body problem in the quantum scattering theory. Jerusalem: Israel Program for Scientific Translations 1965
[6]
Faris, W.: Time decay and the Born series. Rocky Mount. J. Math.1, 637?648 (1971)
10.1216/rmj-1971-1-4-637
[7]
Ginibre, J., Moulin, M.: Hilbert space approach to the quantum mechanical three-body problem. Ann. Inst. Henri Poincaré A21, 97?145 (1974)
[8]
Hagedorn, G.A.: Asymptotic completeness for classes of two, three, and four particle Schrödinger operators. Ph.D. Thesis, Princeton University (to appear)
[9]
Herbst, I.W.: Unitary equivalence of Stark hamiltonians. Math. Z.155, 55?70 (1977)
10.1007/bf01322607
[10]
Howland, J.S.: Abstract stationary theory of multichannel scattering. J. Funct. Anal.22, 250?282 (1976)
10.1016/0022-1236(76)90012-4
[11]
Ikebe, T.: Eigenfunctions associated with the Schrödinger operators and their applications to scattering theory. Arch. Rat. Mech. Anal.5, 1?34 (1960)
10.1007/bf00252896
[12]
Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966
[13]
Merkuriev, S.P., Gignoux, C., Laverne, A.: Three body scattering in configuration space. Ann. Phys.99, 30?71 (1977)
10.1016/0003-4916(76)90083-x
[14]
Povsner, A. Ya: On the expansion of arbitrary functions in terms of the eigenfunctions of the operator ??u+cu. Am. Math. Soc. Trans., 2nd Ser.60, 1?49 (1967)
10.1090/trans2/060/01
[15]
Rauch, J.: Local decay of scattering solutions to Schrödinger's equation. Commun. Math. Phys.61, 149?168 (1978)
10.1007/bf01609491
[16]
Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. II: Fourier analysis, self-adjointness. New York: Academic Press 1975
[17]
Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. III: Scattering theory. New York-London: Academic Press (to appear)
[18]
Schechter, M.: A new criterion for scattering theory. Duke Math. J.44, 863?877 (1977)
10.1215/s0012-7094-77-04439-8
[19]
Sigal, I.M.: Mathematical foundations of quantum scattering theory for multiparticle systems. Preprint, Tel-Aviv University (1975)
[20]
Simon, B.: Quantum mechanics for hamiltonians defined as quadratic forms. Princeton: Princeton University Press 1971
[21]
Simon, B.: Absence of positive eigenvalues in a class of multiparticle quantum systems. Math. Ann.207, 133?138 (1974)
10.1007/bf01362152
[22]
Simon, B.: Scattering theory and quadratic forms: on a theorem of Schechter. Commun. Math. Phys.53, 151?153 (1977)
10.1007/bf01609129
[23]
Thomas, L.E.: Asymptotic completeness in two- and three-particles quantum mechanical scattering. Ann. Phys.90, 127?165 (1975)
10.1016/0003-4916(75)90143-8
[24]
Zemach, C., Klein, A.: The Born expansion in non-relativistic quantum theory. Nuovo Cimento10, 1078?1087 (1958)
10.1007/bf02859570
Metrics
4
Citations
24
References
Details
- Published
- Feb 01, 1979
- Vol/Issue
- 66(1)
- Pages
- 77-94
- License
- View
Authors
Cite This Article
George A. Hagedorn (1979). Born series for (2 cluster) ? (2 cluster) scattering of two, three, and four particle Schr�dinger operators. Communications in Mathematical Physics, 66(1), 77-94. https://doi.org/10.1007/bf01197746
Related
You May Also Like
Intermittent transition to turbulence in dissipative dynamical systems
Yves Pomeau, PAUL MANNEVILLE · 1980
1,701 citations