×

zbMATH — the first resource for mathematics

Solution of the Schrödinger equation in terms of classical paths. (English) Zbl 0281.35029

MSC:
35J10 Schrödinger operator, Schrödinger equation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Strutinsky, V.M.; Strutinsky, V.M.; Nilsson, S.G.; Tsang, C.F.; Sobiczewski, A.; Szymánski, Z.; Wycech, S.; Gustafsson, C.; Lamm, I.L.; Möller, P.; Nilsson, B.; Dietrich, K., (), A 131, 373, (1969)
[2] {\scA. Michaudon}, Advances in Nucl. Phys.{\bf6}, 1; {\scJ. R. Nix}, Ann. Rev. Nucl. Sci.{\bf22}, 65.
[3] Balian, R.; Bloch, C.; Balian, R.; Bloch, C.; Balian, R.; Bloch, C., Ann. phys. (N.Y.), Ann. phys. (N.Y.), Ann. phys. (N.Y.), 69, 76, (1972), hereafter referred to as I, II, III
[4] Balian, R.; De Dominicis, C., Ann. phys. (N.Y.), 62, 229, (1971), Appendix C, giving a perturbative treatment valid even in the region of the poles of G
[5] Keller, J.B.; Rubinow, S.I.; Arnold, V.I.; Miller, W.H.; Pechukas, P., Ann. phys. (N.Y.), Funct. anal. appl., J. chem. phys., J. chem. phys., 57, 5577, (1972)
[6] Falicov, L.M.; Stachowiak, H.; Pippard, A.B., (), 147, 113, (1966)
[7] Baraff, G.A.; Borowitz, S.; Stephen, M.J.; Zalewski, K.; Payne, H.; Kohn, W.; Sham, L.J.; Thorpe, M.A.; Thouless, D.J.; Miller, W.H., (), Phys. rev., Phys. rev. A, Nucl. phys., J. chem. phys., 56, 38, (1972)
[8] Gutzwiller, M.; Gutzwiller, M.; Gutzwiller, M.; Gutzwiller, M., J. math. phys., J. math. phys., J. math. phys., J. math. phys., 12, 343, (1971)
[9] Berry, M.V.; Mount, K.E., Rep. progr. phys., 35, 315, (1972), Extensive references on the semiclassical methods may be found in the recent review article by
[10] Balian, R.; Bloch, C., Ann. phys. (N.Y.), 63, 592, (1971), the present work is a continuation of this paper, hereafter referred to as I’
[11] Kompaneets, A.S.; Pavlovskii, E.S.; Kirzhnits, D.A.; Kirzhnits, D.A.; Golden, S.; Golden, S.; DuBois, D.F.; Kivelson, M.G.; Hohenberg, P.; Kohn, W., Field theoretical methods in many-body systems, Soviet physics JETP, Soviet physics JETP, Phys. rev., Rev. mod. phys., Phys. rev., Phys. rev. B, 136, 864, (1966), Pergamon Oxford
[12] Heading, J.; Fröman, N.; Fröman, P.O., JWKB approximation, (1965), Methuen London, Amsterdam · Zbl 0129.41907
[13] Keller, J.B.; Pokrovskii, V.L.; Khalatnikov, I.N.; Patashinskii, A.Z.; Pokrovskii, V.L.; Khalatnikov, I.M.; Patashinskii, A.Z.; Pokrovskii, V.L.; Khalatnikov, I.M.; Patashinskii, A.Z.; Pokrovskii, V.L.; Khalatnikov, I.M.; Maslov, V.P.; Perelomov, A.M.; Popov, V.S.; Terentiev, M.V.; Kotova, L.P.; Perelomov, A.M.; Popov, V.S.; Norcliffe, A.; Percival, I.C.; Roberts, M.J.; Norcliffe, A.; Percival, I.C.; Roberts, M.J.; Percival, I.C.; Freed, K.F., (), J. chem. phys., 56, 692, (1972)
[14] Goldman, I.I.; Migdal, A.B.; Ford, K.W.; Wheeler, J.A.; Ford, K.W.; Wheeler, J.A.; Newton, R.G.; Pechukas, P.; Pechukas, P., Scattering theory of waves and particles, Soviet physics JETP, Ann. phys. (N.Y.), Ann. phys. (N.Y.), Phys. rev., Phys. rev., 181, 174, (1969), McGraw-Hill New York, Chapter 18
[15] Child, M.S.; Crothers, D.S.F.; Broglia, R.A.; Winther, A., Molecular phys., Adv. phys., Physics reports, 4C, 153, (1972)
[16] Marcus, R.A., J. chem. phys., 54, 3965, (1971)
[17] Ludwig, D.; Rubinow, S.I.; Keller, J.B., Comm. pure appl. math., Phys. rev., 131, 2789, (1963)
[18] Pokrovskii, V.L.; Savvinnykh, S.K.; Ulinich, F.R.; Pokrovskii, V.L.; Savvinnykh, S.K.; Ulinich, F.R., Soviet physics JETP, Soviet physics JETP, 7, 1119, (1958)
[19] Maslov, V.P.; Maslov, V.P., Original in Russian, (1965), Dunod Paris, Moscow · Zbl 0528.47034
[20] Dagens, L., J. physique, 30, 593, (1969)
[21] Norcliffe, A.; Percival, I.C.; Norcliffe, A.; Percival, I.C.; Schulman, L.; DeWitt, C.; Norcliffe, A.; Percival, I.C.; Roberts, M.J.; Norcliffe, A.; Percival, I.C.; Roberts, M.J.; Dowker, J.S.; Norcliffe, A.; Norcliffe, A.; Norcliffe, A., J. phys. B, J. phys. B, Phys. rev., Ann. inst. Poincaré, J. phys. B, J. phys. B, J. phys. A, J. phys. B, J. phys. A, J. phys. A, 6, L127, (1973)
[22] Friedel, J., Philos. mag., 43, 153, (1952)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.