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Commutators and scattering theory. I: Repulsive interactions. (English) Zbl 0207.13706


MSC:

35P25 Scattering theory for PDEs
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47A40 Scattering theory of linear operators
47B47 Commutators, derivations, elementary operators, etc.

Keywords:

228.35071

Citations:

Zbl 0216.385
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Full Text: DOI

References:

[1] Amrein, W. O., Martin, P. A., Misra, B.: On the asymptotic condition of scattering theory, preprint, University of Geneva. · Zbl 0195.56101
[2] Combes, J. M.: An algebraic approach to quantum scattering theory, preprint C.P.T., C.N.R.S., Marseille.
[3] Dollard, J. D.: Asymptotic convergence and the Coulomb interaction. J. Math. Phys.5, 729–738 (1964). · doi:10.1063/1.1704171
[4] —- Adiabatic switching in the Schrödinger theory of scattering. J. Math. Phys.7, 802–810 (1966). · doi:10.1063/1.1931210
[5] —- Screening in the Schrödinger theory of scattering, J. Math. Phys.9, 620–624 (1968). · doi:10.1063/1.1664618
[6] —- Scattering into cones I: potential scattering, Commun. Math. Phys.12, 193–203 (1969). · doi:10.1007/BF01661573
[7] – Notes on Coulomb scattering, to appear, Rocky Mountain Math. J.
[8] Hepp, K.: On the quantum mechanicalN-body problem. Helv. Phys. Acta42, 425–459 (1969).
[9] Kato, T.: Wave operators and similarity for some non-self-adjoint operators, Math. Ann.162, 258–279 (1966). · Zbl 0139.31203 · doi:10.1007/BF01360915
[10] —- Smooth operators and commutators. Studia Math. T.XXXI, 535–546 (1968). · Zbl 0215.48802
[11] Lavine, R. B.: Absolute continuity of Hamiltonian operators with repulsive potential, Proc. Am. Math. Soc.22, 55–60 (1969). · Zbl 0176.45801
[12] —- Scattering theory for long range potentials, J. Funct. Anal.5, 368–382 (1970). · Zbl 0192.61201 · doi:10.1016/0022-1236(70)90015-7
[13] Putnam, C. R.: Commutation properties of Hilbert space operators and related topics. Berlin-Heidelberg-New York: Springer 1967. · Zbl 0149.35104
[14] Riesz, B., Szent-Nagy, B.: Functional Analysis. New York: Ungar 1955.
[15] Weidmann, J.: Zur Spektraltheorie von Sturm-Liouville Operatoren. Math. Z.98, 268–302 (1967). · Zbl 0168.12301 · doi:10.1007/BF01112407
[16] —- The virial theorem and its application to the spectral theory of Schrödinger operators. Bull. Am. Math. Soc.73, 452–456 (1967). · Zbl 0156.23304 · doi:10.1090/S0002-9904-1967-11781-6
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