Ikot, A. N.; Okon, I. B.; Okorie, U. S.; Omugbe, E.; Abdel-Aty, A. -H.; Obagboye, L. F.; Ahmadov, A. I.; Okpara, N.; Duque, C. A.; Abdullah, Hewa Y.; Qadir, Karwan W. Exact solutions of position-dependent mass Schrödinger equation with pseudoharmonic oscillator and its thermal properties using extended Nikiforov-Uvarov method. (English) Zbl 1533.34004 Z. Angew. Math. Phys. 75, No. 1, Paper No. 18, 20 p. (2024). MSC: 34A05 34L40 33C47 × Cite Format Result Cite Review PDF Full Text: DOI
Doğan Çalışır, Ayşe; Turan, Mehmet; Sevinik Adıgüzel, Rezan Spectrum of a \(q\)-deformed Schrödinger equation by means of the variational method. (English) Zbl 1536.34080 Math. Methods Appl. Sci. 46, No. 18, 18693-18705 (2023). MSC: 34L40 34L15 05A30 81Q05 33D45 11B65 × Cite Format Result Cite Review PDF Full Text: DOI
Boyack, Rufus; Bhuiyan, Asadullah; Su, Aneca; Marsiglio, Frank The bound-state solutions of the one-dimensional pseudoharmonic oscillator. (English) Zbl 1518.81043 J. Math. Chem. 61, No. 1, 242-276 (2023). MSC: 81Q05 34L40 31A05 33C05 47A52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liu, Xiao-Ming; Tian, Xiao-Ping; Hong, Ling; Shu, Yue Periodic solutions of Mathieu oscillator, induced by fuzzy uncertainty. (English) Zbl 07912212 Lacarbonara, Walter (ed.) et al., Advances in nonlinear dynamics. Proceedings of the second international nonlinear dynamics conference, NODYCON 2021, virtual event, February 16–19, 2021. Volume 3. Cham: Springer. NODYCON Conf. Proc. Ser., 605-615 (2022). MSC: 34L40 34A07 34C28 34C25 × Cite Format Result Cite Review PDF Full Text: DOI
Grishechkin, Yu. A.; Kapshai, V. N. Approximate analytic solution of the Logunov-Tavkhelidze equation for a one-dimensional oscillator potential in the relativistic configuration representation. (English. Russian original) Zbl 1515.81090 Theor. Math. Phys. 211, No. 3, 826-837 (2022); translation from Teor. Mat. Fiz. 211, No. 3, 455-468 (2022). MSC: 81Q05 34B24 34L40 34A45 × Cite Format Result Cite Review PDF Full Text: DOI
Khanmamedov, Agil Kh.; Muradov, Mammad F. To the inverse spectral problem for a perturbed oscillator on the semiaxis. (English) Zbl 1487.34061 Proc. Inst. Math. Mech., Natl. Acad. Sci. Azerb. 48, No. 1, 104-112 (2022). MSC: 34A55 34L40 × Cite Format Result Cite Review PDF
Huseynov, Hidayat M.; Abbasova, Khatira E. On the completeness of the system of Weber functions. (English) Zbl 1513.34355 Trans. Natl. Acad. Sci. Azerb., Ser. Phys.-Tech. Math. Sci. 41, No. 4, Math., 78-82 (2021). MSC: 34L40 34B09 34L15 × Cite Format Result Cite Review PDF Full Text: Link
Khanmamedov, Agil K.; Gafarova, Nigar F. Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition. (English) Zbl 1483.34029 J. Inverse Ill-Posed Probl. 29, No. 5, 675-688 (2021). Reviewer: Namig Guliyev (Baku) MSC: 34A55 34B09 34L40 34L05 × Cite Format Result Cite Review PDF Full Text: DOI
Baumann, Gerd Sinc methods for Lévy-Schrödinger equations. (English) Zbl 1476.34015 Beghin, Luisa (ed.) et al., Nonlocal and fractional operators. Selected papers based on the presentations at the international workshop, Rome, Italy, April 12–13, 2019. Cham: Springer. SEMA SIMAI Springer Ser. 26, 23-56 (2021). MSC: 34A08 34L40 34B24 34L15 34L16 26A33 × Cite Format Result Cite Review PDF Full Text: DOI
Jafarov, E. I.; Nagiyev, S. M.; Seyidova, A. M. PDEM Schrödinger equation with Gora-Williams kinetic energy operator. (English) Zbl 1513.81042 Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 82, No. 1, 327-336 (2020). MSC: 81Q05 34L40 33C45 34A05 81Q80 × Cite Format Result Cite Review PDF
Khanmamedov, A. Kh.; Masmaliev, G. M.; Gafarova, N. F. Towards the spectral theory of a perturbed oscillator on the half-axis. (Russian) Zbl 1474.34599 J. Contemp. Appl. Math. 10, No. 1, 58-63 (2020). MSC: 34L05 34L10 34A55 34L40 × Cite Format Result Cite Review PDF Full Text: Link
Chargui, Yassine Extended Dirac oscillator in (2 + 1)-dimensional space-time. (English) Zbl 1448.81303 Phys. Lett., A 384, No. 25, Article ID 126484, 4 p. (2020). MSC: 81Q05 34L40 35Q41 × Cite Format Result Cite Review PDF Full Text: DOI
Jafarov, E. I.; Nagiyev, S. M.; Jafarova, A. M. Quantum-mechanical explicit solution for the confined harmonic oscillator model with the von Roos kinetic energy operator. (English) Zbl 1451.81229 Rep. Math. Phys. 86, No. 1, 25-37 (2020). MSC: 81Q05 34L40 33C45 34A05 × Cite Format Result Cite Review PDF Full Text: DOI
Kazakov, Konstantin V. Integrable anharmonic potentials for stretching and bending molecular vibrations. (English) Zbl 1433.81094 Ann. Phys. 414, Article ID 168096, 16 p. (2020). MSC: 81Q80 81Q05 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Gromov, N. A.; Kuratov, V. V. Harmonic oscillator on Minkowski plane. (Russian. English summary) Zbl 1430.81030 Vestn. Syktyvkar. Univ., Ser. 1, Mat. Mekh. Inform. 27, No. 2, 10-23 (2018). MSC: 81Q10 34L40 83A05 70H40 × Cite Format Result Cite Review PDF
Bagirova, Sevinj M.; Khanmamedov, Agil H. The inverse spectral problem for the perturbed harmonic oscillator on the entire axis. (English) Zbl 1454.34035 Proc. Inst. Math. Mech., Natl. Acad. Sci. Azerb. 44, No. 2, 285-294 (2018). MSC: 34A55 34L40 34C15 34L05 × Cite Format Result Cite Review PDF
Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F. Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis. (English. Russian original) Zbl 1401.81047 Theor. Math. Phys. 195, No. 1, 538-547 (2018); translation from Teor. Mat. Fiz. 195, No. 1, 54-63 (2018). MSC: 81Q05 81U40 34L40 34L25 × Cite Format Result Cite Review PDF Full Text: DOI
Mahmudova, M. G.; Khanmamedov, A. Kh. On an inverse spectral problem for a perturbed harmonic oscillator. (English) Zbl 1402.34019 Azerb. J. Math. 8, No. 2, 181-191 (2018). Reviewer: Xiangdong Yang (Kunming) MSC: 34A55 34L40 34B09 34B40 × Cite Format Result Cite Review PDF
Castro, L. B.; Obispo, A. E. Generalized relativistic harmonic oscillator in minimal length quantum mechanics. (English) Zbl 1370.81069 J. Phys. A, Math. Theor. 50, No. 28, Article ID 285202, 10 p. (2017). MSC: 81Q10 81R60 70H40 81R20 34B24 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Mityagin, Boris S. The spectrum of a harmonic oscillator operator perturbed by \(\delta\)-interactions. (English) Zbl 1353.47085 Integral Equations Oper. Theory 85, No. 4, 451-495 (2016). MSC: 47E05 34L40 34L15 × Cite Format Result Cite Review PDF Full Text: DOI
Killingbeck, J. P.; Jolicard, G.; Grosjean, A. The cubic oscillator revisited. (English) Zbl 1342.81110 J. Phys. A, Math. Theor. 49, No. 10, Article ID 108001, 4 p. (2016). MSC: 81Q05 34L40 81Q10 × Cite Format Result Cite Review PDF Full Text: DOI
Boulton, Lyonell; Hobiny, Aatef On the quality of complementary bounds for eigenvalues. (English) Zbl 1331.65107 Calcolo 52, No. 4, 577-601 (2015). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65L15 65L60 34L16 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J. Pseudospectra in non-Hermitian quantum mechanics. (English) Zbl 1328.81116 J. Math. Phys. 56, No. 10, 103513, 32 p. (2015). Reviewer: Roman V. Romanov (St. Petersburg) MSC: 81Q20 47E05 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Amore, Paolo; Fernández, Francisco M. Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials. (English) Zbl 1331.81087 J. Math. Chem. 53, No. 6, 1351-1362 (2015). MSC: 81Q05 82C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Homorodean, Laurean A new approach to one-dimensional oscillators in relativistic quantum mechanics. (English) Zbl 1312.81064 Transylv. J. Math. Mech. 6, No. 1, 17-28 (2014). MSC: 81Q05 81Q80 81Q10 70H40 × Cite Format Result Cite Review PDF
Hiroshima, Fumio; Sasaki, Itaru Spectral analysis of non-commutative harmonic oscillators: the lowest eigenvalue and no crossing. (English) Zbl 1315.34090 J. Math. Anal. Appl. 415, No. 2, 595-609 (2014). MSC: 34L15 47E05 81Q10 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Amir, Naila; Iqbal, Shahid Exact solutions of Schrödinger equation for the position-dependent effective mass harmonic oscillator. (English) Zbl 1308.81072 Commun. Theor. Phys. 62, No. 6, 790-794 (2014). MSC: 81Q05 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Ferreira, E. M.; Sesma, J. Global solution of the cubic oscillator. (English) Zbl 1302.81094 J. Phys. A, Math. Theor. 47, No. 41, Article ID 415306, 21 p. (2014). MSC: 81Q05 34L40 81Q10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bidasyuk, Y.; Vanroose, W. Improved convergence of scattering calculations in the oscillator representation. (English) Zbl 1284.65092 J. Comput. Phys. 234, 60-78 (2013). MSC: 65L20 65L12 81V05 34L40 34D05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gaudreau, Philippe; Slevinsky, Richard M.; Safouhi, Hassan An asymptotic expansion for energy eigenvalues of anharmonic oscillators. (English) Zbl 1286.81079 Ann. Phys. 337, 261-277 (2013). MSC: 81Q10 81Q20 34E05 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wakayama, Masato Simplicity of the lowest eigenvalue of non-commutative harmonic oscillators and the Riemann scheme of a certain Heun’s differential equation. (English) Zbl 1278.34099 Proc. Japan Acad., Ser. A 89, No. 6, 69-73 (2013). MSC: 34L15 34L40 81Q10 34M05 81S05 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Hamzavi, M.; Ikhdair, S. M.; Thylwe, K.-E. Equivalence of the empirical shifted Deng-Fan oscillator potential for diatomic molecules. (English) Zbl 1269.81224 J. Math. Chem. 51, No. 1, 227-238 (2013). MSC: 81V55 81Q05 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Adduci, James; Mityagin, Boris Eigensystem of an \(L ^{2}\)-perturbed harmonic oscillator is an unconditional basis. (English) Zbl 1259.47059 Cent. Eur. J. Math. 10, No. 2, 569-589 (2012). Reviewer: Manfred Möller (Johannesburg) MSC: 47E05 34L40 34L10 47A10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, D.-Y.; Huang, M.-J. Dirichlet operators with convex potentials on the half-line. (English) Zbl 1240.34440 Acta Math. Hung. 130, No. 1-2, 195-201 (2011). Reviewer: Mihai Pascu (Bucuresti) MSC: 34L15 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Helffer, B. The Montgomery model revisited. (English) Zbl 1207.34110 Colloq. Math. 118, No. 2, 391-400 (2010). Reviewer: Chie-Ping Chu (Taipei) MSC: 34L05 34L15 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Asaithambi, Asai Numerical solution of the one-dimensional time-independent Schrödinger’s equation by recursive evaluation of derivatives. (English) Zbl 1186.65098 Appl. Math. Comput. 215, No. 12, 4400-4405 (2010). MSC: 65L10 34B05 34L40 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Znojil, Miloslav Imaginary cubic oscillator and its square-well approximations in \(x\)- and \(p\)-representation. (English) Zbl 1215.34110 Int. J. Math. Game Theory Algebra 18, No. 4-5, 315-330 (2009). Reviewer: Satyanad Kichenassamy (Reims) MSC: 34L40 81Q05 × Cite Format Result Cite Review PDF Full Text: arXiv
Sazonov, S. V. Motion of quantum anharmonic oscillator. (Russian. English summary) Zbl 1185.81079 Uch. Zap. Kazan. Gos. Univ., Ser. Fiz.-Mat. Nauki 151, No. 1, 150-157 (2009). MSC: 81Q05 81R30 34L40 × Cite Format Result Cite Review PDF
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. A phase-fitted symplectic partitioned Runge-Kutta methods for the numerical solution of the Schrödinger equation. (English) Zbl 1182.65127 Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics, Rethymno, Crete, Greece, September 18–22, 2009. Vol. 2. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0708-4/hbk; 978-0-7354-0709-1/set). AIP Conference Proceedings 1168, 2, 1595-1599 (2009). MSC: 65L15 34L16 34L40 65P10 37M15 65L06 65L70 × Cite Format Result Cite Review PDF Full Text: DOI
Cohen-Tannoudji, Claude; Diu, Bernard; Laloë, Frank Quantum mechanics. Vol. 1. Translated from the French original by Joachim v. Streubel and Jochen Balla. 4th revised ed. (Quantenmechanik. Band 1. Übersetzt aus dem Französischen von Joachim v. Streubel und Jochen Balla.) (German) Zbl 1170.81003 Berlin: de Gruyter (ISBN 978-3-11-021519-9/hbk). xviii, 722 p. (2009). Reviewer: Claudia-Veronika Meister (Darmstadt) MSC: 81-01 × Cite Format Result Cite Review PDF Full Text: DOI
Fujii, Kazuyuki; Suzuki, Tatsuo General solution of the quantum damped harmonic oscillator. II: Some examples. (English) Zbl 1166.81014 Int. J. Geom. Methods Mod. Phys. 6, No. 2, 225-231 (2009). MSC: 81Q05 81R30 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liu, Jianjun; Zhai, Lixue Using the finite difference method to solve the energy eigenvalue equation. (Chinese. English summary) Zbl 1174.65443 J. Beijing Univ. Technol. 34, No. 3, 325-331 (2008). MSC: 65L15 81Q05 65L12 34L16 34L40 × Cite Format Result Cite Review PDF
Parmeggiani, Alberto On the spectrum of certain non-commutative harmonic oscillators and semiclassical analysis. (English) Zbl 1168.47038 Commun. Math. Phys. 279, No. 2, 285-308 (2008). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 47E05 34L40 35S05 47G30 47N50 81Q20 × Cite Format Result Cite Review PDF Full Text: DOI
Endo, Ryusuke; Fujii, Kazuyuki; Suzuki, Tatsuo General solution of the quantum damped harmonic oscillator. (English) Zbl 1151.81328 Int. J. Geom. Methods Mod. Phys. 5, No. 5, 653-661 (2008). MSC: 81Q05 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pişcoran, Laurian The noncommutative Dirac equation for some wave functions. (English) Zbl 1199.81011 Acta Univ. Apulensis, Math. Inform. 13, 71-74 (2007). Reviewer: Mihai Pascu (Bucureşti) MSC: 81Q05 34L40 58B99 × Cite Format Result Cite Review PDF Full Text: EuDML
Gana, Sameh; Mhadbi, Noureddine Pseudo-spectra of the complex harmonic oscillator. (English) Zbl 1148.34055 Glob. J. Pure Appl. Math. 3, No. 2, 151-165 (2007). Reviewer: Zoran Kadelburg (Beograd) MSC: 34L40 34L20 81Q20 × Cite Format Result Cite Review PDF
Voros, André From exact-WKB toward singular quantum perturbation theory. II. (English) Zbl 1139.81348 Aoki, Takashi (ed.) et al., Algebraic analysis of differential equations. From microlocal analysis to exponential asymptotics. Festschrift in honor of Takahiro Kawai. Containing papers presented at the conference on algebraic analysis of differential equations–from microlocal analysis to exponential asymptotics, Kyoto, Japan, July 7–14, 2005. Tokyo: Springer (ISBN 978-4-431-73239-6/hbk). 321-334 (2007). MSC: 81Q20 34E20 34L40 81Q15 × Cite Format Result Cite Review PDF Full Text: arXiv
Hilger, Stefan The discrete and periodic heat and harmonic oscillator equation. (English) Zbl 1132.39013 J. Difference Equ. Appl. 13, No. 8-9, 741-793 (2007). Reviewer: Zhibo Huang (Guangzhou) MSC: 39A12 34L40 35K05 42A16 33C45 × Cite Format Result Cite Review PDF Full Text: DOI
Parmeggiani, Alberto On the spectrum of certain noncommutative harmonic oscillators. (English) Zbl 1144.34055 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 52, No. 2, 431-456 (2006). Reviewer: Manfred Möller (Johannesburg) MSC: 34L05 34L20 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Nedelec, Laurence Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators. (English) Zbl 1125.34068 Methods Appl. Anal. 13, No. 1, 123-148 (2006). Reviewer: Manfred Möller (Johannesburg) MSC: 34L05 34D10 34L40 34L20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pravda-Starov, Karel A complete study of the pseudo-spectrum for the rotated harmonic oscillator. (English) Zbl 1106.34060 J. Lond. Math. Soc., II. Ser. 73, No. 3, 745-761 (2006). Reviewer: Mihai Pascu (Bucureşti) MSC: 34L40 47A10 35S99 × Cite Format Result Cite Review PDF Full Text: DOI
Turbiner, Alexander Anharmonic oscillator and double-well potential: Approximating eigenfunctions. (English) Zbl 1092.34049 Lett. Math. Phys. 74, No. 2, 169-180 (2005). Reviewer: Vadim Komkov (Florida) MSC: 34L40 34B08 41A99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hilger, Stefan The harmonic oscillator – an extension via measure chains. (English) Zbl 1117.39321 Elaydi, Saber (ed.) et al., Proceedings of the 8th international conference on difference equations and applications (ICDEA 2003), Masaryk University, Brno, Czech Republic, July 28–August 1, 2003. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-536-X/hbk). 155-170 (2005). MSC: 39A12 39A70 34L40 65L15 × Cite Format Result Cite Review PDF
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. Trigonometrically and exponentially fitted symplectic methods of third order for the numerical integration of the Schrödinger equation. (English) Zbl 1075.65146 ANACM, Appl. Numer. Anal. Comput. Math. 2, No. 2, 238-244 (2005). MSC: 65P10 37M15 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E. Exponentially fitted symplectic methods for the numerical integration of the Schrödinger equation. (English) Zbl 1073.65071 J. Math. Chem. 37, No. 3, 263-270 (2005). MSC: 65L15 34L16 34L40 65P10 37M15 × Cite Format Result Cite Review PDF Full Text: DOI
Ivanov, I. A. Transformation of the asymptotic perturbation expansion for the anharmonic oscillator into a convergent expansion. (English) Zbl 1118.81370 Phys. Lett., A 322, No. 3-4, 194-204 (2004). MSC: 81Q15 34L40 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Chelkak, Dmitri; Kargaev, Pavel; Korotyaev, Evgeni Inverse problem for harmonic oscillator perturbed by potential, characterization. (English) Zbl 1085.81055 Commun. Math. Phys. 249, No. 1, 133-196 (2004). Reviewer: Maksim Sokolov (Tashkent) MSC: 81U40 34A55 34L40 81Q10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Chelkak, Dmitri; Kargaev, Pavel; Korotyaev, Evgeni Inverse problem for harmonic oscillator perturbed by potential. (English) Zbl 1073.34013 Isozaki, Hiroshi (ed.), Inverse problems and spectral theory. Proceedings of the workshop on spectral theory of differential operators and inverse problems, Kyoto University, Kyoto, Japan, October 28–November 1, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3421-5/pbk). Contemporary Mathematics 348, 93-102 (2004). Reviewer: Michael Baro (Berlin) MSC: 34A55 34L40 81Q10 30D55 × Cite Format Result Cite Review PDF
Taşeli, H. Accurate numerical bounds for the spectral points of singular Sturm–Liouville problems over \(0 < x <\infty\). (English) Zbl 1037.81040 J. Comput. Appl. Math. 164-165, 707-722 (2004). MSC: 81Q10 81-08 81Q05 65L15 42C10 34L40 34B30 33C55 81V45 81V55 × Cite Format Result Cite Review PDF Full Text: DOI
Chelkak, Dmitri; Kargaev, Pavel; Korotyaev, Evgeni An inverse problem for an harmonic oscillator perturbed by potential: uniqueness. (English) Zbl 1030.34085 Lett. Math. Phys. 64, No. 1, 7-21 (2003). MSC: 34L40 34A55 34C15 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Boulton, Lyonell S. Non self-adjoint harmonic oscillator compact semigroups and pseudospectra. (English) Zbl 1034.34099 J. Oper. Theory 47, No. 2, 413-429 (2002). Reviewer: I. Beltiţă (Bucureşti) MSC: 34L40 47A75 47D06 × Cite Format Result Cite Review PDF Full Text: arXiv
Faria, A. J.; França, H. M.; Malta, C. P.; Sponchiado, R. C. Critical assessment of the Schrödinger picture of quantum mechanics. (English) Zbl 1005.81022 Phys. Lett., A 305, No. 6, 322-328 (2002). MSC: 81P05 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Debergh, N.; Ndimubandi, J.; Van den Bossche, B. A general approach of quasi-exactly solvable Schrödinger equations. (English) Zbl 1005.81021 Ann. Phys. 298, No. 2, 361-381 (2002). MSC: 81Q05 81U15 81Q10 34L40 34L10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sugawara, M. Numerical solution of the Schrödinger equation by neural network and genetic algorithm. (English) Zbl 0990.65088 Comput. Phys. Commun. 140, No. 3, 366-380 (2001). MSC: 65L15 65L20 92B20 68T05 34L40 65P10 37M15 65Y05 × Cite Format Result Cite Review PDF Full Text: DOI
Ochiai, H. Non-commutative harmonic oscillators and Fuchsian ordinary differential operators. (English) Zbl 0982.34070 Commun. Math. Phys. 217, No. 2, 357-373 (2001). Reviewer: Roman Hilscher (East Lansing) MSC: 34L05 34L40 17B81 34C15 70G65 × Cite Format Result Cite Review PDF Full Text: DOI
Álvarez, Gabriel; Howls, Christopher J.; Silverstone, Harris J. Connection formula, hyperasymptotics, and Schrödinger eigenvalues: Dispersive hyperasymptotics and the anharmonic oscillator. (English) Zbl 0990.34073 Howls, Christopher J. (ed.) et al., Toward the exact WKB analysis of differential equations, linear or non-linear. Papers from the symposium on algebraic analysis of singular perturbations, Kyoto, Japan, November 30-December 5, 1998. Kyoto: Kyoto University Press. 121-134 (2000). Reviewer: Shun Shimomura (Yokohama) MSC: 34L40 34E05 34L20 33C10 81Q05 × Cite Format Result Cite Review PDF
Negro, J.; Nieto, L. M.; Rosas-Ortiz, O. Refined factorizations of solvable potentials. (English) Zbl 0963.81071 J. Phys. A, Math. Gen. 33, No. 40, 7207-7215 (2000). MSC: 81U15 81Q05 81R15 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Aslanyan, A.; Davies, E. B. Spectral instability for some Schrödinger operators. (English) Zbl 0964.65076 Numer. Math. 85, No. 4, 525-552 (2000). Reviewer: Waldemar Velte (Würzburg) MSC: 65L15 34L15 34L40 65L07 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Handy, C. R.; Murenzi, R. Continuous wavelet transform analysis of one-dimensional quantum ground states. (English) Zbl 0976.34072 Dubuc, Serge (ed.) et al., Spline functions and the theory of wavelets. Providence, RI: AMS, American Mathematical Society. CRM Proc. Lect. Notes. 18, 303-314 (1999). Reviewer: N.D.Sengupta (Mumbai) MSC: 34L40 81Q05 44A60 × Cite Format Result Cite Review PDF
Slavyanov, Sergei Yu. Multipole moments for Coulomb and oscillator wavefunctions and the Heun equation. (English) Zbl 0928.34070 J. Phys. A, Math. Gen. 32, No. 9, 1773-1778 (1999). MSC: 34L40 81S99 34B24 × Cite Format Result Cite Review PDF Full Text: DOI
Dobrovolska, I. V.; Tutik, R. S. Semiclassical treatment of logarithmic perturbation theory. (English) Zbl 0942.34075 J. Phys. A, Math. Gen. 32, No. 3, 563-568 (1999). MSC: 34L40 81Q20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Davies, E. B. Pseudo-spectra, the harmonic oscillator and complex resonances. (English) Zbl 0931.70016 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 455, No. 1982, 585-599 (1999). MSC: 70J10 34L16 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Hall, Richard L.; Saad, Nasser Eigenvalue bounds for a class of singular potentials in \(N\) dimensions. (English) Zbl 0923.34073 J. Phys. A, Math. Gen. 32, No. 1, 133-138 (1999). MSC: 34L15 34L40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hall, Richard L.; Saad, Nasser; von Keviczky, Attila B. Matrix elements for a generalized spiked harmonic oscillator. (English) Zbl 0935.81015 J. Math. Phys. 39, No. 12, 6345-6352 (1998). MSC: 81Q05 34L40 47N50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Grecchi, Vincenzo; Sacchetti, Andrea Wannier-Bloch oscillators. (English) Zbl 0922.34073 Commun. Math. Phys. 197, No. 3, 553-569 (1998). MSC: 34L40 81Q50 47E05 × Cite Format Result Cite Review PDF Full Text: DOI
Lehninger, Harald; Liu, Yunkang The functional-differential equation \(y'(t) = Ay(t) + By(qt) + Cy'(qt) + f(t)\). (English) Zbl 0918.34062 Eur. J. Appl. Math. 9, No. 1, 81-91 (1998). MSC: 34K05 81R05 34L40 × Cite Format Result Cite Review PDF Full Text: DOI
Billionnet, C. About poles of the resolvent in a model for a harmonic oscillator coupled with massless scalar bosons. (English) Zbl 0907.34067 Ann. Inst. Henri Poincaré, Phys. Théor. 68, No. 1, 1-16 (1998). Reviewer: P.Dyshlovenko (Ul’yanovsk) MSC: 34L40 81V45 81Q10 47N50 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Bogdanov, Alexander V.; Gevorkyan, Ashot S. New perturbation theory for the nonstationary anharmonic oscillator. (English) Zbl 0938.81010 J. Phys. A, Math. Gen. 30, No. 21, 7413-7425 (1997). Reviewer: N.Parhi (Berhampur) MSC: 81Q15 34L40 34A45 81U40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Um, Chung-In; Kim, In-Han; Yeon, Kyu-Hwang; George, Thomas F.; Pandey, Lakshmi N. Wavefunctions and minimum uncertainty states of the harmonic oscillator with an exponentially decaying mass. (English) Zbl 0927.34066 J. Phys. A, Math. Gen. 30, No. 7, 2545-2556 (1997). MSC: 34L40 81Q05 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Tong, Peiging; Goodings, D. A. Application of Bogomolny’s transfer operator to a circular harmonic oscillator plus \(1/r^2\) potential. (English) Zbl 0926.34069 J. Phys. A, Math. Gen. 30, No. 11, 4065-4073 (1997). MSC: 34L40 81Q20 × Cite Format Result Cite Review PDF Full Text: DOI
Ivanov, I. A. Sum rule for the spectra of \(x^{2m}\) potentials. (English) Zbl 0918.34075 J. Phys. A, Math. Gen. 30, No. 12, 4337-4339 (1997). MSC: 34L40 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Bay, Karlheinz; Lay, Wolfgang; Akopyan, Alexey Avoided crossings of the quartic oscillator. (English) Zbl 0917.34072 J. Phys. A, Math. Gen. 30, No. 9, 3057-3067 (1997). MSC: 34L40 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Skála, L.; Dvořák, J.; Kapsa, V. Analytic solutions of the Schrödinger equation for the modified quartic oscillator. (English) Zbl 0901.34097 Int. J. Theor. Phys. 36, No. 12, 2953-2961 (1997). MSC: 34L40 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Mavromatis, Harry A. A straightforward mapping of the arbitrary-dimensional Coulomb problem into the isotropic oscillator. (English) Zbl 0895.34066 Rep. Math. Phys. 40, No. 1, 17-19 (1997). MSC: 34L40 81Q99 × Cite Format Result Cite Review PDF Full Text: DOI
Bessis, N.; Bessis, G. Open perturbation and the Riccati equation: Algebraic determination of the quartic anharmonic oscillator energies and eigenfunctions. (English) Zbl 0888.34070 J. Math. Phys. 38, No. 11, 5483-5492 (1997). MSC: 34L40 81Q15 × Cite Format Result Cite Review PDF Full Text: DOI
Ntibashirakandi, L. Supersymmetric spectra of the Calogero problem. (English) Zbl 0882.34085 Bull. Soc. R. Sci. Liège 66, No. 5, 365-377 (1997). MSC: 34L40 81Q60 81Q05 × Cite Format Result Cite Review PDF
Braun, M.; Sofianos, S. A.; Papageorgiou, D. G.; Lagaris, I. E. An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the Schrödinger equation on a grid. (English) Zbl 0856.65123 J. Comput. Phys. 126, No. 2, 315-327 (1996). Reviewer: V.Burjan (Praha) MSC: 65N25 35P15 35Q55 34L40 81Q05 65L15 × Cite Format Result Cite Review PDF Full Text: DOI
Dobrokhotov, S. Yu.; Olivé, V. M. Lissajoux figures, two-dimensional tori, and spectral series of the three-dimensional anharmonic oscillator. (English. Russian original) Zbl 0866.34073 St. Petersbg. Math. J. 8, No. 2, 273-279 (1997); translation from Algebra Anal. 8, No. 2, 121-128 (1996). MSC: 34L40 × Cite Format Result Cite Review PDF
Dobrokhotov, S. Yu.; Olivé, V. M. Lissajoux figures, two-dimensional tori, and spectral series in the three-dimensional anharmonic oscillator. (Russian) Zbl 0849.34067 Algebra Anal. 8, No. 2, 121-128 (1996). Reviewer: L.A.Sakhnovich (Odessa) MSC: 34L40 × Cite Format Result Cite Review PDF
Martin, V.; Robledo, L. M. Numerical and symbolic calculation of the multipole matrix elements in the axial and triaxial harmonic oscillator basis. (English) Zbl 0926.65071 Comput. Phys. Commun. 99, No. 1, 113-127 (1996). MSC: 65L05 34L40 34-04 81-04 68W30 81V70 × Cite Format Result Cite Review PDF Full Text: DOI
Bagrov, Vladislav G.; Samsonov, Boris F. Coherent states of anharmonic oscillator Hamiltonians with equidistant and quasi-equidistant spectra. (English) Zbl 0917.34070 J. Phys. A, Math. Gen. 29, No. 5, 1011-1023 (1996). MSC: 34L40 81R30 81Q99 × Cite Format Result Cite Review PDF Full Text: DOI
Ivanov, I. A. The harmonic oscillator and Coulomb potentials – two exceptions from the point of view of a function theory. (English) Zbl 0901.34095 J. Phys. A, Math. Gen. 29, No. 12, 3203-3207 (1996). MSC: 34L40 81Q05 34L05 × Cite Format Result Cite Review PDF Full Text: DOI
Skála, Lubomir; Dvořak, Jan Analytical solution of the Schrödinger equation for the modified quartic oscillator. (English) Zbl 0882.34084 Bull. Soc. Sci. Lett. Łódź 46, Sér. Rech. Déform. 22, 5-10 (1996). Reviewer: V.Komkov (Roswell) MSC: 34L40 81Q05 × Cite Format Result Cite Review PDF
Sergeev, A. V. Summation of the eigenvalue perturbation series by multi-valued Padé approximants: Application to resonance problems and double wells. (English) Zbl 0859.34075 J. Phys. A, Math. Gen. 28, No. 14, 4157-4162 (1995). MSC: 34L40 41A21 34L15 34M99 × Cite Format Result Cite Review PDF Full Text: DOI
Bacus, B.; Meurice, Y.; Soemadi, A. Precise determination of the energy levels of the anharmonic oscillator from the quantization of the angle variable. (English) Zbl 0859.34065 J. Phys. A, Math. Gen. 28, No. 14, L381-L385 (1995). MSC: 34L40 34E20 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Komarov, L. I.; Romanova, T. S.; Solodukhin, A. M. Solutions of the Schrödinger equation for a particle in a central field by the operator method. (Russian. English summary) Zbl 0853.65080 Izv. Akad. Nauk Belarusi, Ser. Fiz.-Mat. Nauk 1995, No. 3, 50-55 (1995). Reviewer: P.Chocholatý (Bratislava) MSC: 65L10 81Q05 34L40 × Cite Format Result Cite Review PDF
Budaev, Yu. O.; Karavaev, A. G. Quasiclassical trajectory-coherent states for a Caldirola-Kanai oscillator. (English. Russian original) Zbl 0937.81030 Russ. Phys. J. 38, No. 2, 177-185 (1995); translation from Izv. Vyssh. Uchebn. Zaved., Fiz. 1995, No. 2, 85-89 (1995). MSC: 81R30 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Samsonov, B. F.; Ovcharov, I. N. Darboux transformation and nonclassical orthogonal polynomials. (English. Russian original) Zbl 0944.34070 Russ. Phys. J. 38, No. 4, 378-384 (1995); translation from Izv. Vyssh. Uchebn. Zaved., Fiz. 1995, No. 4, 58-65 (1995). MSC: 34L40 81Q05 33C45 34A05 34A25 44A15 × Cite Format Result Cite Review PDF Full Text: DOI
Samsonov, B. F.; Ovcharov, I. N. Darboux transformation and exactly solvable potentials with quasi-equidistant spectrum. (English. Russian original) Zbl 0942.34073 Russ. Phys. J. 38, No. 8, 765-771 (1995); translation from Izv. Vyssh. Uchebn. Zaved., Fiz. 1995, No. 8, 3-10 (1995). MSC: 34L40 81U05 34A05 44A15 81Q05 × Cite Format Result Cite Review PDF Full Text: DOI
Dobrokhotov, Sergeiĭ Yu.; Martínez-Olivé, Victor; Shafarevich, Andreĭ I. Closed trajectories and two-dimensional tori in the quantum problem for a three-dimensional resonant anharmonic oscillator. (English) Zbl 0907.34070 Russ. J. Math. Phys. 3, No. 1, 133-138 (1995). MSC: 34L40 81Q20 34E20 × Cite Format Result Cite Review PDF