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Educ 72(11):1015. doi:10.1021/ed072p1015, http://dx.doi.org/10.1021/ed072p1015
17. Siegert AJF (1939) On the derivation of the dispersion formula for nuclear reactions.
Phys Rev 56:750–752. doi:10.1103/PhysRev.56.750, http://link.aps.org/doi/10.1103/
PhysRev.56.750
18. Hatano N, Sasada K, Nakamura H, Petrosky T (2008) Some properties of the resonant state in
quantum mechanics and its computation. Prog Theor Phys 119(2):187–222. doi:10.1143/
PTP.119.187, http://ptp.oxfordjournals.org/content/119/2/187.abstract
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dilatation-analytic interactions. Commun Math Phys 22(4):280–294
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and the foundations of time-dependent perturbation theory. Ann Math 97:247–274
22. Simon B (1979) The definition of molecular resonance curves by the method of
exterior complex scaling. Phys Lett A 71(2):211–214
23. Ho Y (1983) The method of complex coordinate rotation and its applications to atomic
collision processes. Phys Rep 99(1):1–68. doi:10.1016/0370-1573(83)90112-6, http://www.
sciencedirect.com/science/article/pii/0370157383901126
24. McCurdy CW, Baertschy M, Rescigno TN (2004) Solving the three-body Coulomb breakup
problem using exterior complex scaling. J Phys B At Mol Opt 37(17):R137, http://stacks.iop.
org/0953-4075/37/i ¼ 17/a ¼ R01
25. Moiseyev N (1998) Quantum theory of resonances: calculating energies, widths and crosssections by complex scaling. Phys Rep 302(5–6):212–293. doi:10.1016/S0370-1573(98)
00002-7, http://www.sciencedirect.com/science/article/pii/S0370157398000027
26. Reinhardt WP (1982) Complex coordinates in the theory of atomic and molecular structure
and dynamics. Annu Rev Phys Chem 33(1):223–255. doi:10.1146/annurev.pc.33.100182.
001255, http://www.annualreviews.org/doi/abs/10.1146/annurev.pc.33.100182.001255
27. Simon B (1978) Resonances and complex scaling: a rigorous overview. Int J Quantum Chem
14(4):529–542. doi:10.1002/qua.560140415, http://dx.doi.org/10.1002/qua.560140415
28. Cerjan C, Hedges R, Holt C, Reinhardt WP, Scheibner K, Wendoloski JJ (1978) Complex
coordinates and the Stark effect. Int J Quantum Chem 14(4):393–418. doi:10.1002/qua.
560140408, http://dx.doi.org/10.1002/qua.560140408
29. Herbst IW (1979) Dilation analyticity in constant electric field. Commun Math Phys 64(3):
279–298. doi:10.1007/BF01221735
30. Herbst IW, Simon B (1978) Stark effect revisited. Phys Rev Lett 41:67–69. doi:10.1103/
PhysRevLett.41.67, http://link.aps.org/doi/10.1103/PhysRevLett.41.67
31. Scrinzi A, Piraux B (1998) Two-electron atoms in short intense laser pulses. Phys Rev A 58:
1310–1321. doi:10.1103/PhysRevA.58.1310, http://link.aps.org/doi/10.1103/PhysRevA.58.1310
32. Junker BR (1983) Complex virial theorem and complex scaling. Phys Rev A 27:2785–2789.
doi:10.1103/PhysRevA.27.2785, http://link.aps.org/doi/10.1103/PhysRevA.27.2785
33. Moiseyev N, Friedland S, Certain PR (1981) Cusps, θ trajectories, and the complex virial
theorem. J Chem Phys 74(8):4739–4740. doi:10.1063/1.441624, http://scitation.aip.org/content/aip/journal/jcp/74/8/10.1063/1.441624
34. McCurdy CW (1980) Complex-coordinate calculation of matrix elements of the resolvent of
the Born–Oppenheimer Hamiltonian. Phys Rev A 21:464–470. doi:10.1103/PhysRevA.21.
464, http://link.aps.org/doi/10.1103/PhysRevA.21.464
35. McCurdy CW, Rescigno TN (1978) Extension of the method of complex basis functions to
molecular resonances. Phys Rev Lett 41:1364–1368. doi:10.1103/PhysRevLett.41.1364,
http://link.aps.org/doi/10.1103/PhysRevLett.41.1364
Dynamical Processes in Open Quantum Systems from a TDDFT Perspective:. . .
267
1123–1135. doi:10.1103/PhysRev.178.1123, http://link.aps.org/doi/10.1103/PhysRev.178.1123
16. Gellene GI (1995) Resonant states of a one-dimensional piecewise constant potential. J Chem
Educ 72(11):1015. doi:10.1021/ed072p1015, http://dx.doi.org/10.1021/ed072p1015
17. Siegert AJF (1939) On the derivation of the dispersion formula for nuclear reactions.
Phys Rev 56:750–752. doi:10.1103/PhysRev.56.750, http://link.aps.org/doi/10.1103/
PhysRev.56.750
18. Hatano N, Sasada K, Nakamura H, Petrosky T (2008) Some properties of the resonant state in
quantum mechanics and its computation. Prog Theor Phys 119(2):187–222. doi:10.1143/
PTP.119.187, http://ptp.oxfordjournals.org/content/119/2/187.abstract
19. Aguilar J, Combes J (1971) A class of analytic perturbations for one-body Schr€ odinger
Hamiltonians. Commun Math Phys 22:269–279. doi:10.1007/BF01877510, http://dx.doi.
org/10.1007/BF01877510
20. Balslev E, Combes JM (1971) Spectral properties of many-body Schr€ odinger operators with
dilatation-analytic interactions. Commun Math Phys 22(4):280–294
21. Simon B (1973) Resonances in n-body quantum systems with dilatation analytic potentials
and the foundations of time-dependent perturbation theory. Ann Math 97:247–274
22. Simon B (1979) The definition of molecular resonance curves by the method of
exterior complex scaling. Phys Lett A 71(2):211–214
23. Ho Y (1983) The method of complex coordinate rotation and its applications to atomic
collision processes. Phys Rep 99(1):1–68. doi:10.1016/0370-1573(83)90112-6, http://www.
sciencedirect.com/science/article/pii/0370157383901126
24. McCurdy CW, Baertschy M, Rescigno TN (2004) Solving the three-body Coulomb breakup
problem using exterior complex scaling. J Phys B At Mol Opt 37(17):R137, http://stacks.iop.
org/0953-4075/37/i ¼ 17/a ¼ R01
25. Moiseyev N (1998) Quantum theory of resonances: calculating energies, widths and crosssections by complex scaling. Phys Rep 302(5–6):212–293. doi:10.1016/S0370-1573(98)
00002-7, http://www.sciencedirect.com/science/article/pii/S0370157398000027
26. Reinhardt WP (1982) Complex coordinates in the theory of atomic and molecular structure
and dynamics. Annu Rev Phys Chem 33(1):223–255. doi:10.1146/annurev.pc.33.100182.
001255, http://www.annualreviews.org/doi/abs/10.1146/annurev.pc.33.100182.001255
27. Simon B (1978) Resonances and complex scaling: a rigorous overview. Int J Quantum Chem
14(4):529–542. doi:10.1002/qua.560140415, http://dx.doi.org/10.1002/qua.560140415
28. Cerjan C, Hedges R, Holt C, Reinhardt WP, Scheibner K, Wendoloski JJ (1978) Complex
coordinates and the Stark effect. Int J Quantum Chem 14(4):393–418. doi:10.1002/qua.
560140408, http://dx.doi.org/10.1002/qua.560140408
29. Herbst IW (1979) Dilation analyticity in constant electric field. Commun Math Phys 64(3):
279–298. doi:10.1007/BF01221735
30. Herbst IW, Simon B (1978) Stark effect revisited. Phys Rev Lett 41:67–69. doi:10.1103/
PhysRevLett.41.67, http://link.aps.org/doi/10.1103/PhysRevLett.41.67
31. Scrinzi A, Piraux B (1998) Two-electron atoms in short intense laser pulses. Phys Rev A 58:
1310–1321. doi:10.1103/PhysRevA.58.1310, http://link.aps.org/doi/10.1103/PhysRevA.58.1310
32. Junker BR (1983) Complex virial theorem and complex scaling. Phys Rev A 27:2785–2789.
doi:10.1103/PhysRevA.27.2785, http://link.aps.org/doi/10.1103/PhysRevA.27.2785
33. Moiseyev N, Friedland S, Certain PR (1981) Cusps, θ trajectories, and the complex virial
theorem. J Chem Phys 74(8):4739–4740. doi:10.1063/1.441624, http://scitation.aip.org/content/aip/journal/jcp/74/8/10.1063/1.441624
34. McCurdy CW (1980) Complex-coordinate calculation of matrix elements of the resolvent of
the Born–Oppenheimer Hamiltonian. Phys Rev A 21:464–470. doi:10.1103/PhysRevA.21.
464, http://link.aps.org/doi/10.1103/PhysRevA.21.464
35. McCurdy CW, Rescigno TN (1978) Extension of the method of complex basis functions to
molecular resonances. Phys Rev Lett 41:1364–1368. doi:10.1103/PhysRevLett.41.1364,
http://link.aps.org/doi/10.1103/PhysRevLett.41.1364
Dynamical Processes in Open Quantum Systems from a TDDFT Perspective:. . .
267