extended abstracts 2010
  

written for
Mathematical Reviews
(review journal of AMS)


  • 10. 12. 2010
    MR2677509 Ergun, Ebru; Saglam, Mesude On the metric of a non-Hermitian model. Rep. Math. Phys. 65 (2010), no. 3, 367--378. 81Q80 (34L05 81Q12)
    ( here in pdf and here in pdf, zipped)

  • 10. 12. 2010
    MR2657537 Grandati, Y.; Bérard, A. Rational solutions for the Riccati-Schrödinger equations associated to translationally shape invariant potentials. Ann. Physics 325 (2010), no. 6, 1235--1259. 81Q60 (81Q80)
    ( here in pdf and here in pdf, zipped)

  • 10. 12. 2010
    MR2643633 Jin, Shi; Wu, Hao; Yang, Xu; Huang, Zhongyi Bloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials. J. Comput. Phys. 229 (2010), no. 13, 4869--4883. 82B10 (65Mxx 81Q10)
    ( here in pdf and here in pdf, zipped)

  • 10. 12. 2010
    MR2610110 Motavalli, Hossein; Rezaei Akbarieh, Amin Exact solutions of the Klein-Gordon equation for the scarf-type potential via Nikiforov-Uvarov method. Internat. J. Theoret. Phys. 49 (2010), no. 5, 979--987. 81Q05
    ( here in pdf and here in pdf, zipped)

  • 18. 10. 2010
    MR2639961 Oyewumi, K. J. Realization of the spectrum generating algebra for the generalized Kratzer potentials. Internat. J. Theoret. Phys. 49 (2010), no. 6, 1302--1316. 81V55
    ( here in pdf and here in pdf, zipped)

  • 12. 10. 2010
    MR2666950 Andrianov, A. A.; Cannata, F.; Sokolov, A. V. Spectral singularities for non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity. J. Math. Phys. 51 (2010), no. 5, 052104, 22 pp. 81Q12 (34L10 34L40 47A10 47E05 47N50)
    ( here in pdf and here in pdf, zipped)

  • 12. 10. 2010
    MR2662467 Das, Ashok; Greenwood, L. An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: examples. J. Math. Phys. 51 (2010), no. 4, 042103, 11 pp. 81Q12
    ( here in pdf and here in pdf, zipped)

  • 5. 9. 2010
    MR2608272 Golovaty, Yu. D.; Hryniv, R. O. On norm resolvent convergence of Schrödinger operators with $\delta'$-like potentials. J. Phys. A 43 (2010), no. 15, 155204, 14 pp. 81Qxx (34L40 47E05)
    ( here in pdf and here in pdf, zipped)

  • 5. 9. 2010
    MR2601810 Bender, Carl M.; Mannheim, Philip D. ${\scr{PT}}$ symmetry and necessary and sufficient conditions for the reality of energy eigenvalues. Phys. Lett. A 374 (2010), no. 15-16, 1616--1620. 81Q12
    ( here in pdf and here in pdf, zipped)

  • 12. 8. 2010
    MR2599802 Ghosh, Pijush K. On the construction of a pseudo-Hermitian quantum system with a pre-determined metric in the Hilbert space. J. Phys. A 43 (2010), no. 12, 125203, 19 pp. 81Qxx
    ( here in pdf and here in pdf, zipped)

  • 12. 8. 2010
    MR2599805 Yekken, R.; Lombard, R. J. Energy-dependent potentials and the problem of the equivalent local potential. J. Phys. A 43 (2010), no. 12, 125301, 17 pp. 81Q05 (81P05)
    ( here in pdf and here in pdf, zipped)

  • 6. 8. 2010
    MR2592328 Gavrilik, A. M.; Rebesh, A. P. Polynomially deformed oscillators as $k$-bonacci oscillators. J. Phys. A 43 (2010), no. 9, 095203, 15 pp. 33D15 (81Q05)
    ( here in pdf and here in pdf, zipped)

  • 1. 8. 2010
    MR2605019 Gu, Xiao-Yan; Sun, Jian-Qiang Any $\ell$-state solutions of the Hulthén potential in arbitrary dimensions. J. Math. Phys. 51 (2010), no. 2, 022106, 6 pp. 81Q05
    ( here in pdf and here in pdf, zipped)

  • 8. 7. 2010
    MR2586146 Cannata, Francesco; Ventura, Alberto Reflectionless $\scr{PT}$-symmetric potentials in the one-dimensional Dirac equation. J. Phys. A 43 (2010), no. 7, 075305, 19 pp. 81Q12
    ( here in pdf and here in pdf, zipped)

  • 8. 7. 2010
    MR2564076 Jaramillo, Benjamín; Martínez-y-Romero, R. P.; Núñez-Yépez, H. N.; Salas-Brito, A. L. On the one-dimensional Coulomb problem. Phys. Lett. A 374 (2009), no. 2, 150--153. 81Q60
    ( here in pdf and here in pdf, zipped)

  • 28. 6. 2010
    MR2604610 Stel'makh, S. N. On the composition of numerical methods for solving three-point difference equations. (Russian) Vestsi Nats. Akad. Navuk Belarusi Ser. Fiz.-Mat. Navuk 2009, no. 2, 17--23, 125. 65Q10
    ( here in pdf and here in pdf, zipped)

  • 31. 5. 2010
    MR2591177 Qiang, Wen-Chao; Chen, Wen Li; Li, Kai; Zhang, Hua-Ping Improved arbitrary $l$-state solutions of the Hulthén potential. Internat. J. Modern Phys. A 24 (2009), no. 28-29, 5523--5529. 81Q05
    ( here in pdf and here in pdf, zipped)

  • 31. 5. 2010
    MR2575622 Zhang, Min-Cang; Sun, Guo-Hua; Dong, Shi-Hai Exactly complete solutions of the Schrödinger equation with a spherically harmonic oscillatory ring-shaped potential. Phys. Lett. A 374 (2010), no. 5, 704--708. 81Q05
    ( here in pdf and here in pdf, zipped)

  • 21. 5. 2010
    MR2546703 Panahi, H.; Jahangiry, L. Shape invariant and Rodrigues solution of the Dirac-shifted oscillator and Dirac-Morse potentials. Internat. J. Theoret. Phys. 48 (2009), no. 11, 3234--3240. 81Qxx
    ( here in pdf and here in pdf, zipped)

  • 21. 5. 2010
    MR2511516 O'Shea, Michael J. Harmonic and anharmonic behaviour of a simple oscillator. European J. Phys. 30 (2009), no. 3, 549--558. 81Q05
    ( here in pdf and here in pdf, zipped)

  • 13. 5. 2010
    MR2591149 Lavagno, A. Basic-deformed quantum mechanics. Rep. Math. Phys. 64 (2009), no. 1-2, 79--91. 81R50 (33D90 81Q65)
    ( here in pdf and here in pdf, zipped)

  • 27. 4. 2010
    MR2539246 Khare, Avinash; Dmitriev, Sergey V.; Saxena, Avadh Exact static solutions of a generalized discrete $\phi\sp 4$ model including short-periodic solutions. J. Phys. A 42 (2009), no. 14, 145204, 23 pp. 81T10
    ( here in pdf and here in pdf, zipped)

  • 25. 4. 2010
    MR2563310 Makowski, Adam J. Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem. Ann. Physics 324 (2009), no. 12, 2465--2472. 81Q05 (81Rxx)
    ( here in pdf and here in pdf, zipped)

  • 8. 4. 2010
    MR2552015 Gadella, M.; Heras, F. J. H.; Negro, J.; Nieto, L. M. A delta well with a mass jump. J. Phys. A 42 (2009), no. 46, 465207, 11 pp. 81Q05
    ( here in pdf and here in pdf, zipped)

  • 7. 4. 2010
    MR2552469 Bagchi, Bijan; Fring, Andreas Minimal length in quantum mechanics and non-Hermitian Hamiltonian systems. Phys. Lett. A 373 (2009), no. 47, 4307--4310. 81Q12 (81S05)
    ( here in pdf and here in pdf, zipped)

  • 17. 3. 2010
    MR2546044 Assis, Paulo E. G.; Fring, Andreas From real fields to complex Calogero particles. J. Phys. A 42 (2009), no. 42, 425206, 14 pp. 81Qxx
    ( here in pdf and here in pdf, zipped)

  • 17. 3. 2010
    MR2546046 Grecchi, Vincenzo; Maioli, Marco; Martinez, André Padé summability of the cubic oscillator. J. Phys. A 42 (2009), no. 42, 425208, 17 pp. 81Qxx (34L40 41A21)
    ( here in pdf and here in pdf, zipped)

  • 16. 3. 2010
    MR2573124 Hone, A. N. W.; Senthilvelan, M. Note on the Poisson structure of the damped oscillator. J. Math. Phys. 50 (2009), no. 10, 102902, 7 pp. 81Qxx (81Sxx)
    ( here in pdf and here in pdf, zipped)

  • 5. 3. 2010
    MR2560826 Nash, Patrick L.; Weideman, J. A. C. High accuracy representation of the free propagator. Appl. Numer. Math. 59 (2009), no. 12, 2937--2949. 81Q05 (65F30)
    ( here in pdf and here in pdf, zipped)

  • 5. 3. 2010
    MR2545636 Kraenkel, R. A.; Senthilvelan, M. On the solutions of the position-dependent effective mass Schrödinger equation of a nonlinear oscillator related with the isotonic oscillator. J. Phys. A 42 (2009), no. 41, 415303, 10 pp. 81Qxx
    ( here in pdf and here in pdf, zipped)

  • 5. 3. 2010
    MR2525490 Killingbeck, J. P. A Hill-series approach to wavefunction nodes. J. Phys. A 42 (2009), no. 8, 085302, 12 pp. 81Q05 (81V45)
    ( here in pdf and here in pdf, zipped)

  • 22. 2. 2010
    MR2540389 Su, Wang-Chang Algebraic shape invariant potentials as the generalized deformed oscillator. J. Phys. A 42 (2009), no. 38, 385202, 17 pp. 81Q05
    ( here in pdf and here in pdf, zipped)

  • 16. 2. 2010
    MR2534521 Compean, C. B.; Kirchbach, M. Momentum space trigonometric Rosen-Morse potential. J. Phys. A 42 (2009), no. 36, 365301, 5 pp. 81Qxx (33C55)
    ( here in pdf and here in pdf, zipped)

  • 6. 2. 2010
    MR2538823 Bendix, Oliver; Fleischmann, Ragnar; Kottos, Tsampikos; Shapiro, Boris: Exponentially fragile $\scr{PT}$ symmetry in lattices with localized eigenmodes. Phys. Rev. Lett. 103 (2009), no. 3, 030402, 4 pp. 81Txx (82Bxx)
    ( here in pdf and here in pdf, zipped)

  • 5. 2. 2010
    MR2533897 Bender, Carl M.; Besseghir, Karim; Jones, Hugh F.; Yin, Xinghui Small-$\epsilon$ behavior of the non-Hermitian $\scr P\scr T$-symmetric Hamiltonian $H=p\sp 2+x\sp 2(ix)\sp \epsilon$. J. Phys. A 42 (2009), no. 35, 355301, 10 pp. 81Qxx
    ( here in pdf and here in pdf, zipped)
    and ( here in final form

  • 1. 2. 2010
    MR2525281 Nishimura, Hiromichi; Ogilvie, Michael The large-N limit of PT-symmetric O(N) models. J. Phys. A 42 (2009), no. 2, 02202, 9 pp. 81Qxx
    ( here in pdf and here in pdf, zipped)

  • 22. 1. 2010
    MR2525883 Fellows, Jonathan M.; Smith, Robert A. Factorization solution of a family of quantum nonlinear oscillators. J. Phys. A 42 (2009), no. 33, 335303, 13 pp. 81Q05
    ( here in pdf and here in pdf, zipped)

  • 20. 1. 2010
    MR2534061 Pahlavani, M. R.; Sadeghi, J.; Ghezelbash, M. Solutions of the central Woods-Saxon potential in $l\neq 0$ case using mathematical modification method. Appl. Sci. 11 (2009), 106--113. 81Q05 (81V35 83A05)
    ( here in pdf and here in pdf, zipped)

  • 13. 1. 2010
    MR2539256 Rotter, Ingrid: A non-Hermitian Hamilton operator and the physics of open quantum systems. J. Phys. A 42 (2009), no. 15, 153001, 51 pp. 81Qxx
    ( here in pdf and here in pdf, zipped)



jump to the older extended abstracts:

written during 2009;

written during 2008;

written during the years 1999 - 2007