Graffi, Sandro; Yajima, Kenji Exterior complex scaling and the AC-Stark effect in a Coulomb field. (English) Zbl 0522.35085 Commun. Math. Phys. 89, 277-301 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 14 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 35J10 Schrödinger operator, Schrödinger equation 81Q15 Perturbation theories for operators and differential equations in quantum theory 81U99 Quantum scattering theory Keywords:exterior complex scaling; Stark effect; Coulomb field; existence; resonances; time-dependent Schrödinger equation; Fermi Golden Rule × Cite Format Result Cite Review PDF Full Text: DOI Euclid References: [1] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0148.12601 [2] Kato, T.: Wave operators and similarity for some non selfadjoint operators. Math. Ann.162, 258-276 (1966) · Zbl 0139.31203 · doi:10.1007/BF01360915 [3] Kitada, H., Yajima, K.: A scattering theory for time-dependent long-range potentials. Duke Math. J. (to appear) · Zbl 0499.35087 [4] Kisynski, J.: Sur les operateurs de Green des probl?mes de Cauchy abstraits. Stud. Math.23, 285-328 (1964) · Zbl 0117.10202 [5] Lanhoff, P.W., Epstein, S.T., Karplus, M.: Aspects of time-dependent perturbation theory. Rev. Mod. Phys.44, 602-644 (1974) · doi:10.1103/RevModPhys.44.602 [6] Mizohata, S.: Partial differential equations. Cambridge: Cambridge University Press 1973 · Zbl 0263.35001 [7] Reed, M., Simon, B.: Methods of modern mathematical physics, Vols. I?IV. New York: Academic Press 1972, 1975, 1979, 1978 · Zbl 0242.46001 [8] Simon, B.: Quantum mechanics of Hamiltonians defined as quadratic forms. Princeton: Princeton University Press 1972 [9] Simon, B.: The definition of molecular resonance curves by the method of exterior complex scaling. Phys. Lett.71, 211-214 (1979) · doi:10.1016/0375-9601(79)90165-8 [10] Simon, B.: Exterior complex scaling and molecular resonances in the Born-Oppenheimer approximation (to appear) [11] Scully, M.O., Sargent III, M.: The concept of the photon. Phys. Today25, 38-47 (1972) · doi:10.1063/1.3070771 [12] Yajima, K.: Resonances for AC-Stark effect. Commun. Math. Phys.87, 331-352 (1982) · Zbl 0538.47010 · doi:10.1007/BF01206027 [13] Yajima, K.: Scattering theory for Schr?dinger equations with potentials periodic in time. J. Math. Soc. Jpn.29, 729-743 (1977) · Zbl 0356.47010 · doi:10.2969/jmsj/02940729 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.