References analysis of the Wikipedia article "Laplace–Runge

arxiv.org

Curtright, T.; Zachos C. (2003). "Classical and Quantum Nambu Mechanics". Physical Review. D68 (8): 085001. arXiv:hep-th/0212267. Bibcode:2003PhRvD..68h5001C. doi:10.1103/PhysRevD.68.085001. S2CID 17388447.

Zachos, C.; Curtright T. (2004). "Branes, quantum Nambu brackets, and the hydrogen atom". Czech Journal of Physics. 54 (11): 1393–1398. arXiv:math-ph/0408012. Bibcode:2004CzJPh..54.1393Z. doi:10.1007/s10582-004-9807-x. S2CID 14074249.

Nikitin, A G (7 December 2012). "New exactly solvable systems with Fock symmetry". Journal of Physics A: Mathematical and Theoretical. 45 (48): 485204. arXiv:1205.3094. Bibcode:2012JPhA...45V5204N. doi:10.1088/1751-8113/45/48/485204. S2CID 119138270.

doi.org

Pauli, W. (1926). "Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik". Zeitschrift für Physik. 36 (5): 336–363. Bibcode:1926ZPhy...36..336P. doi:10.1007/BF01450175. S2CID 128132824.

Hanca, J.; Tulejab, S.; Hancova, M. (2004). "Symmetries and conservation laws: Consequences of Noether's theorem". American Journal of Physics. 72 (4): 428–35. Bibcode:2004AmJPh..72..428H. doi:10.1119/1.1591764.

Fock, V. (1935). "Zur Theorie des Wasserstoffatoms". Zeitschrift für Physik. 98 (3–4): 145–154. Bibcode:1935ZPhy...98..145F. doi:10.1007/BF01336904. S2CID 123112334.

Bargmann, V. (1936). "Zur Theorie des Wasserstoffatoms: Bemerkungen zur gleichnamigen Arbeit von V. Fock". Zeitschrift für Physik. 99 (7–8): 576–582. Bibcode:1936ZPhy...99..576B. doi:10.1007/BF01338811. S2CID 117461194.

Goldstein, H. (1975). "Prehistory of the Runge–Lenz vector". American Journal of Physics. 43 (8): 737–738. Bibcode:1975AmJPh..43..737G. doi:10.1119/1.9745.
Goldstein, H. (1976). "More on the prehistory of the Runge–Lenz vector". American Journal of Physics. 44 (11): 1123–1124. Bibcode:1976AmJPh..44.1123G. doi:10.1119/1.10202.

Fradkin, D. M. (1967). "Existence of the Dynamic Symmetries O₄ and SU₃ for All Classical Central Potential Problems". Progress of Theoretical Physics. 37 (5): 798–812. Bibcode:1967PThPh..37..798F. doi:10.1143/PTP.37.798.

Yoshida, T. (1987). "Two methods of generalisation of the Laplace–Runge–Lenz vector". European Journal of Physics. 8 (4): 258–259. Bibcode:1987EJPh....8..258Y. doi:10.1088/0143-0807/8/4/005. S2CID 250843588.

Lenz, W. (1924). "Über den Bewegungsverlauf und Quantenzustände der gestörten Keplerbewegung". Zeitschrift für Physik. 24 (1): 197–207. Bibcode:1924ZPhy...24..197L. doi:10.1007/BF01327245. S2CID 121552327.

Evans, N. W. (1990). "Superintegrability in classical mechanics". Physical Review A. 41 (10): 5666–5676. Bibcode:1990PhRvA..41.5666E. doi:10.1103/PhysRevA.41.5666. PMID 9902953.

Evans, N. W. (1991). "Group theory of the Smorodinsky–Winternitz system". Journal of Mathematical Physics. 32 (12): 3369–3375. Bibcode:1991JMP....32.3369E. doi:10.1063/1.529449.

Efimov, S.P. (2022). "Coordinate space modification of Fock's theory. Harmonic tensors in the quantum Coulomb problem". Physics-Uspekhi. 65 (9): 952–967. Bibcode:2022PhyU...65..952E. doi:10.3367/UFNe.2021.04.038966. S2CID 234871720.

Efimov, S.P. (2023). "Runge-Lenz Operator in the Momentum Space". JETP Letters. 117 (9): 716–720. Bibcode:2023JETPL.117..716E. doi:10.1134/S0021364023600635. S2CID 259225778.

Schrödinger, E. (1926). "Quantisierung als Eigenwertproblem". Annalen der Physik. 384 (4): 361–376. Bibcode:1926AnP...384..361S. doi:10.1002/andp.19263840404.

Prince, G. E.; Eliezer C. J. (1981). "On the Lie symmetries of the classical Kepler problem". Journal of Physics A: Mathematical and General. 14 (3): 587–596. Bibcode:1981JPhA...14..587P. doi:10.1088/0305-4470/14/3/009.

Bander, M.; Itzykson C. (1966). "Group Theory and the Hydrogen Atom (I)". Reviews of Modern Physics. 38 (2): 330–345. Bibcode:1966RvMP...38..330B. doi:10.1103/RevModPhys.38.330.

Bander, M.; Itzykson C. (1966). "Group Theory and the Hydrogen Atom (II)". Reviews of Modern Physics. 38 (2): 346–358. Bibcode:1966RvMP...38..346B. doi:10.1103/RevModPhys.38.346.

Rogers, H. H. (1973). "Symmetry transformations of the classical Kepler problem". Journal of Mathematical Physics. 14 (8): 1125–1129. Bibcode:1973JMP....14.1125R. doi:10.1063/1.1666448.

Lakshmanan, M.; Hasegawa H. (1984). "On the canonical equivalence of the Kepler problem in coordinate and momentum spaces". Journal of Physics A. 17 (16): L889–L893. Bibcode:1984JPhA...17L.889L. doi:10.1088/0305-4470/17/16/006.

Redmond, P. J. (1964). "Generalization of the Runge–Lenz Vector in the Presence of an Electric Field". Physical Review. 133 (5B): B1352–B1353. Bibcode:1964PhRv..133.1352R. doi:10.1103/PhysRev.133.B1352.

Dulock, V. A.; McIntosh H. V. (1966). "On the Degeneracy of the Kepler Problem". Pacific Journal of Mathematics. 19: 39–55. doi:10.2140/pjm.1966.19.39.

Lévy-Leblond, J. M. (1971). "Conservation Laws for Gauge-Invariant Lagrangians in Classical Mechanics". American Journal of Physics. 39 (5): 502–506. Bibcode:1971AmJPh..39..502L. doi:10.1119/1.1986202.

Gonzalez-Gascon, F. (1977). "Notes on the symmetries of systems of differential equations". Journal of Mathematical Physics. 18 (9): 1763–1767. Bibcode:1977JMP....18.1763G. doi:10.1063/1.523486.

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ui.adsabs.harvard.edu

Fock, V. (1935). "Zur Theorie des Wasserstoffatoms". Zeitschrift für Physik. 98 (3–4): 145–154. Bibcode:1935ZPhy...98..145F. doi:10.1007/BF01336904. S2CID 123112334.

Evans, N. W. (1990). "Superintegrability in classical mechanics". Physical Review A. 41 (10): 5666–5676. Bibcode:1990PhRvA..41.5666E. doi:10.1103/PhysRevA.41.5666. PMID 9902953.

Evans, N. W. (1991). "Group theory of the Smorodinsky–Winternitz system". Journal of Mathematical Physics. 32 (12): 3369–3375. Bibcode:1991JMP....32.3369E. doi:10.1063/1.529449.

Einstein, A. (1915). "Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie". Sitzungsberichte der Preussischen Akademie der Wissenschaften. 1915: 831–839. Bibcode:1915SPAW.......831E.

Hall 2013 Proposition 17.25. Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158.

Hall 2013 Proposition 18.7; note that Hall uses a different normalization of the LRL vector. Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158.

Hall 2013 Theorem 18.9. Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158.

Hall 2013, Section 18.4.4. Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158.

Efimov, S.P. (2023). "Runge-Lenz Operator in the Momentum Space". JETP Letters. 117 (9): 716–720. Bibcode:2023JETPL.117..716E. doi:10.1134/S0021364023600635. S2CID 259225778.

Schrödinger, E. (1926). "Quantisierung als Eigenwertproblem". Annalen der Physik. 384 (4): 361–376. Bibcode:1926AnP...384..361S. doi:10.1002/andp.19263840404.

Hall 2013 Proposition 18.12. Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158.

Hall 2013 Theorem 18.14. Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158.

Bander, M.; Itzykson C. (1966). "Group Theory and the Hydrogen Atom (I)". Reviews of Modern Physics. 38 (2): 330–345. Bibcode:1966RvMP...38..330B. doi:10.1103/RevModPhys.38.330.

Bander, M.; Itzykson C. (1966). "Group Theory and the Hydrogen Atom (II)". Reviews of Modern Physics. 38 (2): 346–358. Bibcode:1966RvMP...38..346B. doi:10.1103/RevModPhys.38.346.

Rogers, H. H. (1973). "Symmetry transformations of the classical Kepler problem". Journal of Mathematical Physics. 14 (8): 1125–1129. Bibcode:1973JMP....14.1125R. doi:10.1063/1.1666448.

Hall 2013 Proposition 2.34. Hall, Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158.

Gonzalez-Gascon, F. (1977). "Notes on the symmetries of systems of differential equations". Journal of Mathematical Physics. 18 (9): 1763–1767. Bibcode:1977JMP....18.1763G. doi:10.1063/1.523486.

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Fock, V. (1935). "Zur Theorie des Wasserstoffatoms". Zeitschrift für Physik. 98 (3–4): 145–154. Bibcode:1935ZPhy...98..145F. doi:10.1007/BF01336904. S2CID 123112334.

Efimov, S.P. (2023). "Runge-Lenz Operator in the Momentum Space". JETP Letters. 117 (9): 716–720. Bibcode:2023JETPL.117..716E. doi:10.1134/S0021364023600635. S2CID 259225778.

Laplace–Runge–Lenz vector (English Wikipedia)

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