D. I. Bondar, M. Gnatich, V. Yu. Lazur, “Two-dimensional problem of two Coulomb centers at small intercenter distances”, TMF, 148:2 (2006), 269–287; Theoret. and Math. Phys., 148:2 (2006), 1100

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 148, Number 2, Pages 269–287
DOI: https://doi.org/10.4213/tmf2085 (Mi tmf2085)

This article is cited in 11 scientific papers (total in 11 papers)

Two-dimensional problem of two Coulomb centers at small intercenter distances

D. I. Bondar^a, M. Gnatich^b, V. Yu. Lazur^a

^a Uzhgorod National University
^b Institute of Experimental Physics, Slovak Academy of Sciences

Full-text PDF (489 kB) Citations (11)

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DOI: https://doi.org/10.4213/tmf2085

Abstract: We use analytic methods to analyze the discrete spectrum for the problem $(Z_1eZ_2)_2$ in the united-atom limit $(R\ll1)$ and obtain asymptotic expansions for the quantum defect and energy terms of the system $(Z_1eZ_2)_2$ at small intercenter distances $R$ up to terms of the order $O(R^6)$. We investigate the effect of the dimensionality factor on the energy spectrum of the hydrogen molecular ion H$^+_2$.

Keywords: planar problem of two Coulomb centers, boundary layer phenomena, confluent Heun equation, Mathieu functions, Ince equation.

Received: 28.11.2005
Revised: 19.12.2005

English version:
Theoretical and Mathematical Physics, 2006, Volume 148, Issue 2, Pages 1100–1116
DOI: https://doi.org/10.1007/s11232-006-0104-7

Bibliographic databases:

Language: Russian

Citation: D. I. Bondar, M. Gnatich, V. Yu. Lazur, “Two-dimensional problem of two Coulomb centers at small intercenter distances”, TMF, 148:2 (2006), 269–287; Theoret. and Math. Phys., 148:2 (2006), 1100–1116

Citation in format AMSBIB

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https://doi.org/10.4213/tmf2085

https://www.mathnet.ru/eng/tmf/v148/i2/p269

This publication is cited in the following 11 articles:

Khmara V.M., Hnatic M., Lazur V.Yu., Reity O.K., “Quasicrossings of Potential Curves in the Two-Coulomb-Center Problem”, Eur. Phys. J. D, 72:2 (2018), 39
M. Hnatich, V. M. Khmara, V. Yu. Lazur, O. K. Reity, “The WKB method for the quantum mechanical two-Coulomb-center problem”, Theoret. and Math. Phys., 190:3 (2017), 345–358
M. Hnatič, V.M. Khmara, V.Yu. Lazur, O.K. Reity, Gh. Adam, J. Buša, M. Hnatič, “Quasiclassical Study of the Quantum Mechanical Two-Coulomb-Centre Problem”, EPJ Web of Conferences, 108 (2016), 02028
I.V. Simenog, V.V. Mikhnyuk, Yu.M. Bidasyuk, “Structure and Electrochemical Properties of Aqueous Suspensions of Functionalized Single- and Multiwalled Carbon Nanotubes”, Ukr. J. Phys., 59:4 (2014), 439
I.V. Simenog, V.V. Mikhnyuk, M.V. Kuzmenko, “The Conditions of Stability of Two-Dimensional Quantum Systems of Three Charged Particles”, Ukr. J. Phys., 58:3 (2013), 289
Gonzalez Leon M.A. Mateos Guilarte J. Senosiain M.J. de la Torre Mayado M., “On the Supersymmetric Spectra of Two Planar Integrable Quantum Systems”, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 563, ed. AcostaHumanez P. Finkel F. Kamran N. Olver P., Amer Mathematical Soc, 2012, 73–113
Guseinov I, Aydin R, Bagci A, “Application of complete orthonormal sets of psi(alpha)-exponential-type orbitals to accurate ground and excited states calculations of one-electron diatomic molecules using single-zeta approximation”, Chinese Physics Letters, 25:8 (2008), 2841–2844
D. I. Bondar, M. Hnatich, V. Yu. Lazur, “Symbolic computations for the two-Coulomb-centers problem in the space of arbitrary dimension”, Phys. Part. Nuclei Lett., 5:3 (2008), 255
Bondar DI, Hnatich M, Lazur VY, “The two Coulomb centres problem at small intercentre separations in the space of arbitrary dimension”, Journal of Physics A-Mathematical and Theoretical, 40:8 (2007), 1791–1807
Bondarchuk VV, Shvab IM, Bondar DI, et al, “Simple model of scalar-vector interaction for the relativistic two-center problem”, Physical Review A, 76:6 (2007), 062507
M. A. González León, J. Mateos Guilarte, M. de la Torre Mayado, “Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force”, SIGMA, 3 (2007), 124, 24 pp.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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