Geodesic
Ladder operators for quantum systems confined by dihedral angles
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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We report the identification and construction of raising and lowering operators for the complete eigenfunctions of isotropic harmonic oscillators confined by dihedral angles, in circular cylindrical and spherical coordinates; as well as for the hydrogen atom in the same situation of confinement, in spherical, parabolic and prolate spheroidal coordinates. The actions of such operators on any eigenfunction are examined in the respective coordinates, illustrating the possibility of generating the complete bases of eigenfunctions in the respective coordinates for both physical systems. The relationships between the eigenfunctions in each pair of coordinates, and with the same eigenenergies are also illustrated.
Keywords: Ladder operators; harmonic oscillator; hydrogen atom; confinement in dihedral angles. 
@article{SIGMA_2012_8_a59,
     author = {Eugenio Ley-Koo and Guo-Hua Sun},
     title = {Ladder operators for quantum systems confined by dihedral angles},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a59/}
}
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Eugenio Ley-Koo; Guo-Hua Sun. Ladder operators for quantum systems confined by dihedral angles. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a59/

[1] Abramowitz M., Stegun I.A., Handbook of mathematical functions, with formulas, graphs, and mathematical tables, Dover Publications, New York, 1972 | MR

[2] Bander M., Itzykson C., “Group theory and the hydrogen atom. I”, Rev. Modern Phys., 38 (1966), 330–345 | DOI | MR

[3] Bander M., Itzykson C., “Group theory and the hydrogen atom. II”, Rev. Modern Phys., 38 (1966), 346–358 | DOI | MR

[4] Bargmann V., “Zur Theorie des Wasserstoffatoms, Bemerkungen zur gleichnamigen Arbeit von V. Fock”, Z. Phys., 99 (1936), 576–582 | DOI

[5] Cooper I.L., “An integrated approach to ladder and shift operators for the Morse oscillator, radial Coulomb and radial oscillator potentials”, J. Phys. A: Math. Gen., 26 (1993), 1601–1623 | DOI | MR | Zbl

[6] Coulson C.A., Joseph A., “Spheroidal wave functions for the hydrogen atom”, Proc. Phys. Soc., 90 (1967), 887–893 | DOI

[7] Dong S.H., Factorization method in quantum mechanics, Fundamental Theories of Physics, 150, Springer, Dordrecht, 2007 | MR

[8] Dong S.H., “Interbasis expansions for isotropic harmonic oscillator”, Phys. Lett. A, 376 (2012), 1262–1268 | DOI

[9] Dong S.H., Ma Z.Q., “The hidden symmetry for a quantum system with an infinitely deep square-well potential”, Amer. J. Phys., 70 (2002), 520–521 | DOI | MR | Zbl

[10] Fock V., “Zur Theorie des Wasserstoffatoms”, Z. Phys., 98 (1935), 145–154 | DOI

[11] Gutiérrez-Vega J.C., López-Mariscal C., “Nondiffracting vortex beams with continuous orbital angular momentum order dependence”, J. Opt. A: Pure Appl. Opt., 10 (2008), 015009, 8 pp. | DOI | Zbl

[12] Hakobyan Y.M., Kibler M., Pogosyan G.S., Sissakian A.N., “Generalized oscillator: invariance algebra and interbasis expansions”, Phys. Atomic Nuclei, 61 (1998), 1782–1788 ; arXiv: quant-ph/9712014 | MR

[13] Kalnins E.G., Miller Jr. W., Winternitz P., “The group $\mathrm O(4)$, separation of variables and the hydrogen atom”, SIAM J. Appl. Math., 30 (1976), 630–664 | DOI | MR | Zbl

[14] Kibler M., Mardoyan L.G., Pogosyan G.S., “On a generalized oscillator system: interbasis expansions”, Int. J. Quantum Chem., 63 (1997), 133–148 ; arXiv: quant-ph/9608027 | 3.0.CO;2-D class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[15] Ley-Koo E., “The hydrogen atom confined in semi-infinite spaces limited by conoidal boundaries”, Adv. Quantum Chem., 57 (2009), 79–122 | DOI

[16] Louck J.D., Moshinsky M., Wolf K.B., “Canonical transformations and accidental degeneracy. II. The isotropic oscillator in a sector”, J. Math. Phys., 14 (1973), 696–700 | DOI | MR

[17] Mardoyan L.G., Pogosyan G.S., Sissakian A.N., Ter-Antonyan V.M., “Hidden symmetry, separation of variables and interbasis expansions in the two-dimensional hydrogen atom”, J. Phys. A: Math. Gen., 18 (1985), 455–466 | DOI

[18] Mardoyan L.G., Pogosyan G.S., Sissakian A.N., Ter-Antonyan V.M., “Spheroidal analysis of the hydrogen atom”, J. Phys. A: Math. Gen., 16 (1983), 711–728 | DOI | MR | Zbl

[19] Moshinsky M., Smirnov Y.F., The harmonic oscillator in modern physics, Contemporary Concepts in Physics, 9, Harwood Academic, Amsterdam, 1996 | Zbl

[20] Park D., “Relation between the parabolic and spherical eigenfunctions of hydrogen”, Z. Phys., 159 (1960), 155–157 | DOI | MR

[21] Pauli W., “Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik”, Z. Phys., 36 (1926), 336–363 | DOI | Zbl

[22] Stone A.P., “Some properties of Wigner coefficients and hyperspherical harmonics”, Proc. Cambridge Philos. Soc., 52 (1956), 424–430 | DOI | MR | Zbl

[23] Sun G.H., Superintegrabilidad en ecuaciones diferenciales de la física, Ph.D. thesis, ESFM, IPN, México, 2012

[24] Tater C.B., “Coefficients connecting the {S}tark and field-free wave-functions for hydrogen”, J. Math. Phys., 11 (1970), 3192–3195 | DOI | MR