Abstract:
The Kustaanheimo-Stiefel transformation together with the well-known expansion of the kernel of an isotropic harmonic oscillator is used to generate the atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism. Group theoretical implications of the present problem are briefly discussed. © 1983 American Institute of Physics.
Registro:
Documento: |
Artículo
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Título: | Atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism |
Autor: | Grinberg, H.; Marañon, J.; Vucetich, H. |
Filiación: | Departamento de Química Orgánica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de la Plata, C. C. No. 67, 1900 La Plata, Argentina MCIC CONICET, Argentina
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Año: | 1982
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Volumen: | 78
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Número: | 2
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Página de inicio: | 839
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Página de fin: | 844
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Título revista: | The Journal of Chemical Physics
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ISSN: | 00219606
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PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00219606_v78_n2_p839_Grinberg.pdf |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v78_n2_p839_Grinberg |
Referencias:
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- Goovaerts, M.J., Devreese, J.T., (1972) J. Math. Phys, 13, p. 1070
- Duru, I.H., Kleinert, H., (1979) Phys. Lett. B, 84, p. 185
- Duru, I.H., Keyman, E., (1980), Current ICTP IC/80/129, preprint, Miramare, Triestre (); Sehwinger, J., (1964) J. Math. Phys, 5, p. 1606
- Gerry, C.C., Inomata, A., (1981) Phys. Lett. A, 84, p. 172
- Langer, R.E., (1937) Phys. Rev, 51, p. 669
- Kustaanheimo, P., Stiefel, E., (1965) J. Reine Angew. Math, 218, p. 204
- Chlsholm, C.D.H., (1976) Croup Theoretical Techniques in Quantum Chemistry, , .(Academic, New York)
- The geometrical symmetry we are considering should be distinguished from the dynamical symmetries that lead to the unexpected degeneracies of the energy levels of the hydrogen atom and the isotropic harmonic oscillator; Fock, V., (1935) Z. Phys, 98, p. 145. , (a)
- Bargmann, V., Z. Phys (1936) Z. Phys., 99, p. 576. , (b) 1936 99 576
- Bander, M., Itzykson, C., (1966) Rev. Mod. Phys, 38, pp. 330-346. , (c)
- We implicitly are restricting our considerations on the 0 (4) generators to bound states. For continuum states, it turns out that the dynamical symmetry group is isomorphic to the group of Lorenz transformations in one time and three space dimensions rather than to the group of rotations in four space dimensions. See Ref. 17; Runge, C., (a), Vectoranalysis (Hirzel, Leipzig, 1919), Vol. 1, p. 70; Lenz, W., (1924) Z. Phys, 24, p. 197. , (b)
- Pauli, W., Z. Phys (1926) Z. Phys., 36, p. 336. , (c)., 1926 36 336
- Barut, A., Schneider, C.K.E., Wilson, R., (1979) J. Math. Phys, 20, p. 2244
- DeWitt‐Morette, C., Maheshwari, A., Nelson, B., measure (1979) Phys. Rep, 50, p. 257. , This is not a true “” in the classical sense of theory of integration. See, for instance
- (1977), 2424. , For a review on this topic, see V. P. Popov, CERN preprint TH; (1976) Functional Integrals in Quantum Field Theory and Statistical Physics, , and (Atomizdat, Moscow, )
- Kleinert, H., (1978) Fortschr. Phys, 26, p. 565
- (1978) Collective Field Theory of, , and [formula omitted] He, Berlin preprint FUB‐HEP 14/78, extended version of Erice Lecture Note () edited by A. Zichichi
- Ravndal, F., Toyoda, T., (1967) Nucl. Phys. B, 3, p. 312
- Chen, A.C., (1980) Phys. Rev. A, 22, p. 333
- Linderberg, J., (1981) Int. J. Quantum Chem, 19, p. 237
- Fernández, F.M., Castro, E.A., (private communication); Cizek, J., Paldus, J., (1977) Int. J. Quantum Chem, 12, p. 875
- Chen, A.C., (1981) Phys. Rev. A, 23, p. 1655
- Dingle, R.B., (1953) Proc. Cambridge Philos. Soc, 49, p. 103
- Rowley, N., (1979) J. Phys. A: Math. Gen, 12, p. L7
- Nieto, M.N., (1979) Ann. J. Phys, 47, p. 1067
- Ludena, E.V., (1977) J. Chem. Phys, 66, p. 468
- Ley‐Koo, E., Rubinstein, S., (1980) J. Chem. Phys, 73, p. 887
- Fernandez, F.M., Castro, E.A., (1981) Int. J. Quantum Chem, 19, pp. 521-533. ,
- Aguilera‐Navarro, V.C., Iwamoto, H., Ley‐Koo, E., Zimmerman, A.H., (1981) Nuovo Cimento B, 62, p. 91
Citas:
---------- APA ----------
Grinberg, H., Marañon, J. & Vucetich, H.
(1982)
. Atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism. The Journal of Chemical Physics, 78(2), 839-844.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v78_n2_p839_Grinberg [ ]
---------- CHICAGO ----------
Grinberg, H., Marañon, J., Vucetich, H.
"Atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism"
. The Journal of Chemical Physics 78, no. 2
(1982) : 839-844.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v78_n2_p839_Grinberg [ ]
---------- MLA ----------
Grinberg, H., Marañon, J., Vucetich, H.
"Atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism"
. The Journal of Chemical Physics, vol. 78, no. 2, 1982, pp. 839-844.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v78_n2_p839_Grinberg [ ]
---------- VANCOUVER ----------
Grinberg, H., Marañon, J., Vucetich, H. Atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism. 1982;78(2):839-844.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v78_n2_p839_Grinberg [ ]