Abstract
The eigenfunctions and energies of general dilated Hamiltonians are expanded in powers of the dilatation parameter. These expansions, augmented by stationarity and stability conditions, are used to derive exact sum rules for bound and resonance states. Particular attention is paid to Hamiltonians with potentials which depend on external parameters, such as the nuclear coordinates in molecules, and to self-consistent potentials. The sum rules can be employed in practical computations to improve the quality of the results and may also serve in analyzing the results from approximate calculations.
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Nuttall J and Cohen HL (1969) Phys Rev 188:1542
Balslev E and Combes JM (1971) Comm Math Phys 22:280
Doolen G, Nuttall J and Stagat R (1974) Phys Rev A10:1612
Brändas E and Froehlich P (1977) Phys Rev A16:2201
Yaris R and Winkler P (1978) J Phys B11:1475
Moiseyev N, Certain PR and Weinhold F (1978) Mol Phys 36:1613
Winkler P (1986) Int J Quant Chem S20:147–51
Wang Z, Winkler P, Pickup BT and Elander N (1989) Chem Phys 135:247–253
McCurdy CW, Rescigno TN, Davidson ER and Lauderdale JG (1980) J Chem Phys 73:3268–3273
Mishra M, Goscinski O and Öhrn Y (1983) J Chem Phys 79:5505–5511
Mishra M, Goscinski O and Öhrn Y (1983) J Chem Phys 79:5494–5504
Mishra M, Froelich P and Öhrn Y (1981) Chem Phys Lett 81:339
Simon B (1973) Ann Math 97:247
Cederbaum LS, Tarantelli F and Winkler P (1990) J Phys B: At Mol Opt Phys 23:L747–752
Moiseyev N and Corcoran CT (1979) Phys Rev A20:814
McCurdy CW and Rescigno TN (1973) Phys Rev Lett 41:1364
Lefebvre R and Garcia-Sucre M (1978) Int J Quant Chem S21:377
Dalgarno A (1959) Proc Roy Soc A251:282–299
Dirac PA (1926) Proc Cambridge Phil Soc 26:376
Goldstone J and Gottfried K (1959) Nuovo Cimento 13:849
Ehrenreich H and Cohen MH (1959) Phys Rev 115:786
Thouless DJ (1961) The quantum mechanics of many-body systems. Academic Press, New York and London, p 24–29
Bentley M (1990) Phys Rev A42:1192
Moiseyev N and Certain PR (1979) Mol Phys 37:1621
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Cederbaum, L.S., Winkler, P. Dilatation transformation and sum rules for general potentials including self-consistent field potentials. Theoret. Chim. Acta 88, 257–270 (1994). https://doi.org/10.1007/BF01113618
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DOI: https://doi.org/10.1007/BF01113618