The Schrödinger equation for q-deformed modified Eckart potential was investigated in the presence of minimal length formalism using the approximate new wave function and q-deformed potential. It was reduced to Schrödinger  equation with modified Poschl-Teller potential. This equation was solved using Asymptotic Iteration Method (AIM) to get the energy eigenvalues equation and wave functions. The wave function was used to determined the Rényi entropy of quantum system. Then, the Rényi entropy was used to determine the mass energy parameter, temperature and heat capacity of the black hole for some diatomic molecules. The energy spectra showed that the increase of radial and angular quantum number, potential width, minimal length parameter, and the molecule mass caused the decrease of energy eigenvalues. The radial quantum number and the  parameter had the most effect to the wave functions, the number of waves, and the wavelength. The potential width, radial quantum number, and entropy parameter had the most effect on Rényi entropy, mass energy parameter, temperature and heat capacity of Schwarzschild black hole. The increase of quantum number caused the decrease of Renyi entropy, mass energy parameter, temperature and heat capacity of Schwarzchild black hole, but the increase of d caused the increase of Renyi entropy, mass energy parameter, temperature and heat capacity of Schwarzchild black hole.

Bayrak, O., Boztosun, I., & Ciftci, H. (2007). Exact analytical solutions to the Kratzer potential by the asymptotic iteration method. International Journal of Quantum Chemistry, 107(3), 540-544. https://d1wqtxts1xzle7.cloudfront.net/42027344 .

Hassanabadi, H., Yazarloo, B. H., Ikot, A. N., Salehi, N., & Zarrinkamr, S. (2013). Exact analytical versus numerical solutions of Schrödinger equation for Hua plus modified Eckart potential. Indian journal of Physics, 87(12), 1219-1223. https://d1wqtxts1xzle7.cloudfront.net/33398001.

Ikot, A. N., Akpabio, L. E., & Umoren, E. B. (2010). Exact solution of Schrödinger equation with inverted woods-saxon and Manning-Rosen potentials. Journal of Scientific Research, 3(1), 25-25. https://www.banglajol.info/index.php/JSR/article/download/5310/5128.

Berkdemir, C., & Han, J. (2005). Any l-state solutions of the Morse potential through the Pekeris approximation and Nikiforov–Uvarov method. Chemical physics letters, 409(4-6), 203-207. https://www.sciencedirect.com/science/article/pii/S0009261405006974.

Okon, I. B., Popoola, O., & Isonguyo, C. N. (2017). Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method. Advances in High Energy Physics, 2017. https://www.hindawi.com/journals/ahep/2017/9671816/.

Pekeris, C. L. (1934). The rotation-vibration coupling in diatomic molecules. Physical Review, 45(2), 98. https://journals.aps.org/pr/abstract/10.1103/PhysRev.45.98.

Dong, S. H. (2007). Factorization method in quantum mechanics (Vol. 150). Springer Science & Business Media.

Ahmadov, H. I., Qocayeva, M. V., & Huseynova, N. S. (2017). The bound state solutions of the D-dimensional Schrödinger equation for the Hulthén potential within SUSY quantum mechanics. International Journal of Modern Physics E, 26(05), 1750028. https://www.worldscientific.com/doi/abs/10.1142/S0218301317500288.

Ahmadov, A. I., Naeem, M., Qocayeva, M. V., & Tarverdiyeva, V. A. (2018). Analytical solutions of the Schrödinger equation for the Manning-Rosen plus Hulthén potential within SUSY quantum mechanics. In Journal of Physics: Conference Series (Vol. 965, No. 1, p. 012001). IOP Publishing. https://iopscience.iop.org/article/10.1088/1742-6596/965/1/012001/meta.

Falaye, B. J. (2012). Any ℓ-state solutions of the Eckart potential via asymptotic iteration method. Central European Journal of Physics, 10(4), 960-965. https://link.springer.com/article/10.2478/s11534-012-0047-6.

Bayrak, O., & Boztosun, I. (2007). Analytical solutions to the Hulthén and the Morse potentials by using the asymptotic iteration method. Journal of Molecular Structure: THEOCHEM, 802(1-3),17-21. https://www.sciencedirect.com/science/article/pii/S0166128006006257.

Ikot, A. N., Awoga, O. A., & Antia, A. D. (2013). Bound state solutions of d-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential. Chinese Physics B, 22(2), 020304. https://iopscience.iop.org/article/10.1088/1674-1056/22/2/020304/meta.

Alimohammadi, M., & Hassanabadi, H. (2017). Alternative solution of the gamma-rigid Bohr Hamiltonian in minimal length formalism. Nuclear Physics A, 957, 439-449.

https://www.sciencedirect.com/science/article/pii/S0375947416302706.

Haouat, S. (2014). Schrödinger equation and resonant scattering in the presence of a minimal length. Physics Letters B, 729, 33-38. https://www.sciencedirect.com/science/article/pii/S0370269313010356.

Zhang, J. Z., & Osland, P. (2001). Perturbative aspects of q-deformed dynamics. The European Physical Journal C-Particles and Fields, 20(2), 393-396. https://link.springer.com/article/10.1007/s100520100649.

Lavagno, A., Scarfone, A. M., & Swamy, P. N. (2006). Classical and quantum q-deformed physical systems. The European Physical Journal C-Particles and Fields, 47(1), 253-261. https://link.springer.com/article/10.1140/epjc/s2006-02557-y.

Dianawati, D. A., Suparmi, A., & Cari, C. (2018). Solution of Schrodinger equation with qdeformed momentum in Coulomb potential using hypergeometric method. In AIP Conference Proceedings (Vol. 2014, no. 020071). AIP Publishing. https://aip.scitation.org/doi/pdf/10.1063/1.5054475.

Lerda, A. (1992). Anyons. Berlin: Springer-Verlag.

Strominger, A. (1993). Black hole statistics. Physical review letters, 71(21), 3397. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.71.3397.

Macfarlane, A. J. (1989). On q-analogues of the quantum harmonic oscillator and the quantum group SU (2) q. Journal of Physics A: Mathematical and general, 22(21), 4581. https://iopscience.iop.org/article/10.1088/0305-4470/22/21/020/meta.

Sari, R. A., Suparmi, A., & Cari, C. (2015). Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method. Chinese Physics B, 25(1), 010301. https://iopscience.iop.org/article/10.1088/1674-1056/25/1/010301/meta.

Bonatsos, D., Daskaloyannis, C., & Kolokotronis, P. (1997). Coupled Q-oscillators as a model for vibrations of polyatomic molecules. The Journal of chemical physics, 106(2), 605-609. https://aip.scitation.org/doi/abs/10.1063/1.473189.

Johal, R. S., & Gupta, R. K. (1998). Two parameter quantum deformation of U (2)⊃ U (1) dynamical symmetry and the vibrational spectra of diatomic molecules. International Journal of Modern Physics E, 7(05), 553-557. https://www.worldscientific.com/doi/abs/10.1142/S0218301398000294.

Suparmi, A., Cari, C., & Ma’arif, M. (2020). Study of Bohr–Mottelson with minimal length effect for Q-deformed modified Eckart potential and Bohr–Mottelson with Q-deformed quantum for three-dimensional harmonic oscillator potential. Molecular Physics, 118(13), e1694713. https://www.tandfonline.com/doi/abs/10.1080/00268976.2019.1694713.

Chabab, M., El Batoul, A., Lahbas, A., & Oulne, M. (2016). On γ-rigid regime of the Bohr–Mottelson Hamiltonian in the presence of a minimal length. Physics Letters B, 758, 212-218. https://www.sciencedirect.com/science/article/pii/S0370269316301642.

Sprenger, M., Nicolini, P., & Bleicher, M. (2012). Physics on Smallest Scales - An Introduction to Minimal Length Phenomenology. European Journal of Physics, 33(4), 853–862. https://arxiv.org/pdf/1202.1500.pdf.

Garay, L. J. (1995). Quantum gravity and minimum length. International Journal of Modern Physics A, 10(02), 145-165. https://www.worldscientific.com/doi/abs/10.1142/S0217751X95000085.

Bonatsos, D., Lenis, D., Petrellis, D., Terziev, P. A., & Yigitoglu, I. (2006). X (3): an exactly separable γ-rigid version of the X (5) critical point symmetry. Physics Letters B, 632(2-3), 238-242. https://www.sciencedirect.com/science/article/pii/S0370269305015492.

Ciftci, H., Hall, R. L., & Saad, N. (2003). Asymptotic iteration method for eigenvalue problems. Journal of Physics A: Mathematical and General, 36(47), 11807. https://iopscience.iop.org/article/10.1088/0305-4470/36/47/008/meta.

Pratiwi, B. N., Suparmi, A., Cari, C., & Husein, A. S. (2017). Asymptotic iteration method for the modified Pöschl–Teller potential and trigonometric Scarf II non-central potential in the Dirac equation spin symmetry. Pramana, 88(2), 25. https://link.springer.com/content/pdf/10.1007/s12043-016-1326-3.pdf.

Pramono, S., Suparmi, A., & Cari, C. (2016). Relativistic energy analysis of five-dimensional q-deformed radial rosen-morse potential combined with q-deformed trigonometric scarf noncentral potential using asymptotic iteration method. Advances in High Energy Physics, 2016, 1–12. https://arxiv.org/abs/1609.00260.

Hulthen, L., Sugawara, M., & Flugge, S. (1957). Handbuch der Physik. Structure of atomic nuclei, ed. S. Fliigge, 39.

Varshni, Y. P. (1990). Eigenenergies and oscillator strengths for the Hulthén potential. Physical Review A, 41(9), 4682. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.41.4682.

Ikhdair, S. M., & Falaye, B. J. (2014). Bound states of spatially dependent mass Dirac equation with the Eckart potential including Coulomb tensor interaction. The European Physical Journal Plus, 129(1), 1-15. https://link.springer.com/article/10.1140/epjp/i2014-14001-y.

Suparmi, A., Cari, C., & Handhika, J. (2013, April). Approximate solution of Schrodinger equation for Eckart potential combined with Trigonormetric Poschl-teller non-central potential using Romanovski polynomials. In Journal of Physics: Conference Series (Vol. 423, No. 1, p. 012039). IOP Publishing. https://iopscience.iop.org/article/10.1088/1742-6596/423/1/012039/meta.

Darareh, M. D., & Harouni, M. B. (2010). Nonclassical properties of a particle in a finite range trap: The f-deformed quantum oscillator approach. Physics Letters A, 374(40), 4099-4103. https://www.sciencedirect.com/science/article/pii/S0375960110009928.

Arai, A. (1991). Exactly solvable supersymmetric quantum mechanics. Journal of Mathematical Analysis and Applications, 158(1), 63-79. https://www.sciencedirect.com/science/article/pii/0022247X91902674.

Eshghi, M. (2012). Dirac-hyperbolic scarf problem including a coulomb-like tensor potential. Acta Scientiarum. Technology, 34(2), 207-215. https://www.redalyc.org/pdf/3032/303226535011.pdf.

Akpan, I. O., Antia, A. D., & Ikot, A. N. Bound-State Solutions of the Klein-Gordon Equation with-Deformed Equal Scalar and Vector Eckart Potential Using a Newly Improved Approximation Scheme. ISRN High Energy Physics, 2012. https://www.hindawi.com/journals/isrn/2012/798209/.

Eğrifes, H., Demirhan, D., & Büyükkiliç, F. (1999). Polynomial Solutions of the Schrödinger Equation for the “Deformed” Hyperbolic Potentials by

Nikiforov–Uvarov Method. Physica Scripta, 59(2), 90. https://iopscience.iop.org/article/10.1238/Physica.Regular.059a00090/meta.

de Souza Dutra, A. (2005). Mapping deformed hyperbolic potentials into nondeformed ones. Physics Letters A, 339(3-5), 252-254. https://www.sciencedirect.com/science/article/pii/S037596010500383X.

Suparmi, A., Cari, C., & Yuliani, H. (2018). Energy Spectra and Wave Function Analysis of q-Deformed Modified Poschl-Teller and Hyperbolic Scarf II Potentials Using NU Method and a Mapping Method. Advances in Physics Theories and Applications, 2013(16), 64-74. https://doi.org/10.7176/APTA-16-8.

Elviyanti, I. L., Pratiwi, B. N., Suparmi, A., & Cari, C. (2018). The Application of Minimal Length in Klein-Gordon Equation with Hulthen Potential Using Asymptotic Iteration Method. Advances in Mathematical Physics, 2018, 1–8. https://www.hindawi.com/journals/amp/2018/9658679/.

Renyi, A. (1961). Proc. Fourth Berkeley Symp. Math. Stat. Prob. 1960.

Yahya, W. A., Oyewumi, K. J., & Sen, K. D. (2015). Position and momentum information‐theoretic measures of the pseudoharmonic potential. International Journal of Quantum Chemistry, 115(21), 1543-1552. https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.24971.

Czinner, V. G., & Iguchi, H. (2016). Rényi entropy and the thermodynamic stability of black holes. Physics Letters B, 752, 306-310. https://www.sciencedirect.com/science/article/pii/S037026931500917X.

Biró, T. S., & Czinner, V. G. (2013). A q-parameter bound for particle spectra based on black hole thermodynamics with Rényi entropy. Physics Letters B, 726(4-5), 861-865. https://www.sciencedirect.com/science/article/pii/S0370269313007612.

Naderi, L., & Hassanabadi, H. (2016). Bohr Hamiltonian and the energy spectra of the triaxial nuclei. The European Physical Journal Plus, 131(1), 1-6. https://link.springer.com/article/10.1140/epjp/i2016-16005-y.

Bajpai, S.D. (1993). Generating function and orthogonality relations of a class of hypergeometric polynomials. Panamerican Mathematical Journal, 3(1), 95-102. http://www.numdam.org/article/AMBP_1994__1_1_21_0.pdf.

JURNAL PENDIDIKAN FISIKA DAN KEILMUAN by http://e-journal.unipma.ac.id/index.php/JPFK/index is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.