Studying novel 1D potential via the AIM. (English) Zbl 1487.81090
Summary: In this work, we would like to apply the asymptotic iteration method (AIM) to a newly proposed Morse-like deformed potential introduced recently by I. A. Assi et al. [J. Math. Phys. 62, No. 9, 093501, 10 p. (2021; Zbl 1500.81067)] This interesting potential can support bound states and/or resonances. However, in this work, we are only interested in bound states. We considered several choices of the potential parameters and obtained the associated spectrum. Finally, we study the small deformation limit at which this finite spectrum system will transition to infinite spectrum size.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81V45 | Atomic physics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
| 47J26 | Fixed-point iterations |
| 47A10 | Spectrum, resolvent |
Keywords:
Schrödinger equation; bound states; scattering states; 1D Morse potential; asymptotic iteration methodCitations:
Zbl 1500.81067References:
| [1] | Cooper, F., Khare, A. and Sukhatme, U. P., Supersymmetry in Quantum Mechanics (World Scientific, 2001). · Zbl 0988.81001 |
| [2] | Fernández, F. M., Ma, Q. and Tipping, R. H., Phys. Rev. A40, 6149 (1989). |
| [3] | Fernández, F. M., Ma, Q. and Tipping, R. H., Phys. Rev. A39, 1605 (1989). |
| [4] | Fernández, F. M., Frydman, G. I. and Castro, E. A., J. Phys. A: Math. General22, 641 (1989). · Zbl 0677.34025 |
| [5] | Sukhatme, U. and Imbo, T., Phys. Rev. D28, 418 (1983). |
| [6] | Nikiforov, A. F. and Uvarov, V. B., Special Functions of Mathematical Physics, Vol. 205 (Birkhäuser, 1988). · Zbl 0624.33001 |
| [7] | Alhaidari, A. D., J. Math. Phys.58, 072104 (2017). · Zbl 1370.81052 |
| [8] | Alhaidari, A. D. and Bahlouli, H., Phys. Scripta94, 125206 (2019). |
| [9] | Alhaidari, A. D. and Bahlouli, H. and Assi, I. A., Phys. Lett. A380, 1577 (2016). · Zbl 1364.81106 |
| [10] | Assi, I. A., Alhaidari, A. D. and Bahlouli, H., Commun. Theor. Phys.69, 241 (2018). · Zbl 1391.81071 |
| [11] | Alhaidari, A. D., Ann. Phys.317, 152 (2005). · Zbl 1077.81037 |
| [12] | Bahlouli, H. and Alhaidari, A. D., Phys. Scripta81, 025008 (2010). · Zbl 1190.81063 |
| [13] | Ciftci, H., Hall, R. L. and Saad, N., J. Phys. A: Math. General36, 11807 (2003). · Zbl 1070.34113 |
| [14] | Sous, A. J. and Alhaidari, A. D., J. Appl. Math. Phys.4, 79 (2016). |
| [15] | Sous, A. J., J. Appl. Math. Phys.3, 1406 (2015). |
| [16] | Assi, I. A., Sous, A. J. and Ikot, A. N., Eur. Phys. J. Plus132, 525 (2017). |
| [17] | Assi, I. A. and Sous, A. J., Eur. Phys. J. Plus133, 175 (2018). |
| [18] | Assi, I. A., Sous, A. J. and Bahlouli, H., Mod. Phys. Lett. A33, 1850128 (2018). · Zbl 1391.81072 |
| [19] | Sous, A. J., Pramana93, 22 (2019). |
| [20] | Assi, I. A., Sous, A. J. and Bahlouli, H., Eur. Phys. J. Plus135, 1 (2020). |
| [21] | Assi, I. A., Sous, A. J. and Bahlouli, H., Eur. Phys. J. Plus136, 1 (2021). |
| [22] | Alhaidari, A. D., Theor. Math. Phys.206, 84 (2020). |
| [23] | I. A. Assi, A. D. Alhaidari and H. Bahlouli, arXiv:2101.09703. |
| [24] | I. A. Assi, private communication (2021). |
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