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