Study of Klein Gordon Equation with Minimum Length Effect for Woods-Saxon Potetial using Nikiforov-Uvarov Functional Analysis

Windy Andaresta, A Suparmi, C Cari

Abstract

The equation of Klein-Gordon for Woods-Saxon potential was discussed in the minimal length effect. We have found the completion of this equation using an approximation by suggesting a new wave function. The Klein-Gordon equation in minimal length formalism for the Woods-Sadon potential is reduced to the form of the Schrodinger-like equation. Then the equation was accomplished by Nikiforov-Uvarov Functional Analysis (NUFA) with Pekeris approximation. This method is applied to gain the radial eigensolutions with chosen exponential-type potential models. The method of NUFA is more compatible by eliminating vanishing the strict mathematical manipulations found in other methods. The energy calculation results showed that angular momentum, radial quantum number, minimal length parameter, and atomic mass influenced it. The higher the radial quantum number and angular momentum, the lower the energg. In contrast to the the minimal length, the energy will increase in value when the minimal length parameter is enlarged. An increase in atomic mass also causes energy to increase as the radial quantum number and angular momentum are held constant.

Keywords

Klein-Gordon equation; minimal length effecf; Woods-Saxon potential; NUFA method

Full Text:

PDF

References

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

Andaresta, W., Suparmi, A., Cari, C., & Permatahati, L. K. (2020). ‘Study of Klein Gordon equation for modified Woods-Saxon potential using hypergeometric method’. AIP Conference Proceedings. 2296(020132), p. 1-7.

Badalov, V. H., Ahmadov, H. I., & Badalov, S. V. (2010). ‘Any l-state analytical solutions of The Klein-Gordon equation for The Woods-Saxon potential’. Internatonal Journal of Modern Physics E, vol. 19(7), p. 1463-1470.

Bonatsos, D., Lenis, D., Petrellis, D., & Terziev, A. P. (2004). ‘Critical point symmetry for the prolate to oblate nuclear shape phase transition’. Physics Letter B, vol. 588, p. Bs172-B179.

Cari. C., Suparmi, A., & Elviyanti, I. L. (2017). ‘Approximate solution for the minimal length case of Klein Gordon equation for trigonometric cotangent potential using Asymptotic Iteration Method’. Journal of Physics: Conference Series, 909 (012002), p. 1-7.

Chabab, M., Lahbas, A., & Oulne, M. (2012). ‘Analytic L-state solutions of the Klein-Gordon equation for q-deformed Woods-Saxon plus Generalized ring shape potential for the two cases of equal and different mixed vector and scalar potnetials’. International Journal of Modern Physics E, vol. 21, no. 10.

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, vol. 758, p. 212-218.

Dianawati, D. A., Suparmi, A., Cari, C., Anggraini, D., Ulfa, U., Fitri, D. C., & Mega, P. (2018). ‘Hypergeometric method for Klein-Gordon equation with trigonometric Pöschl-Teller and trigonometric Scarf II potentials’. AIP Conference Proceedings 2014 (020164).

Dudek, J., Pomorski, K., Schunck, N., &Dubray, N. (2004). ‘Hyperdeformed and megadeformed nuclei’. The European Physical Journal A, vol. 20, p. 15-29.

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, vol. 2018, p. 1-8.

Feizi, H., Rajabi, A. A., & Shojaei, M. R. (2011). ‘Supersymmetric Solution of the Schrödinger Equation for Woods-Saxon Potential by using the Pekeris Approximation’. ACTA PHYSICA POLONICA B. vol. 42, no. 10, p. 2143-2152.

Freitas, A. S., Marques, L., Zhang, X. X., Luzio, M. A., Guillaumon, P., Pampa Condori, R., & Lichtenthaler, R. (2016) ‘Woods-Saxon equivalent to a double folding potential’. Brazilian Journal of Physics, vol. 46, p. 120-128.

Garay, D.J. (1994). Introduction to Quantum Mechanics. New Jersey: Prentice Hall, p. 29-32.

Hamzavi, M., & Rajabi, A. A., (2013). ‘Generalized Nuclear Woods-Saxon Potential under Relativstic Spin Symmetry Limit ’. Advances in High Energy Physics, vol. 2013, p. 1-7.

Hassanabadi, H., Chung, W. S., Zare, S., & Bhardwaj, S. B. (2017). ‘The Potential Model in High Energy Physics’. Advances in High Energy Physics, vol. 2017, p. 1-4.

Hou, C. F., & Zhou, Z. X. (1999). ‘Bound states of the Klein-Gordon equation with vector and scalar wood-saxon potentials’, Acta Physica Sinica, vol. 8, p. 561-564.

Ikhdair, S. M., & Sever. R. (2007). ’Exact Solution of Klein-Gordon for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method’. Annalen der Physik, vol. 16, no.3, p. 218-232.

Ikot, A. N., Hassanabadi, H., Obong, H. P., Chad Umoren, Y. E., Isonguyo, C. N., & Yazarloo, B. H. (2014). ’Approximate solutions of Klein-Gordon equation with improved Manning-Rosen potential in D-dimensions using SUSYQM’. Chinese Physics B, vol. 23, no. 12.

Ikot, A. N., Okorie, U. S., Rampho, G. J., Amadi, P. O., Edet, C. O., Akpan, I. O., Abdullah, H. Y., & Horchani, R. (2021). ‘Klein-Gordon Equation and Nonrelativistic Thermodynamic Properties with improved Screened Kratzer Potential’. Journal of Low Temperature Physics, vol. 42, no. 10, p. 1-14.

Ikot, A. N., Okorie, U. S., Amadi, P. O., Edet, C. O., Rampho, G. J., & Sever, R. (2021). ‘The Nikiforov-Uvarov-Functional Analysis (NUFA) Method: A New Approach for Solving Exponential-Type Potentials’. Few-Body Systems, vol. 62, no.9, p. 1-16.

Lutfuoglu, B. C., Ikot, A. N., Chukwocha, E. O., & Bazuaye, F. E. (2018). ‘Analytical solution of the Kein Gordon equation with a Multi-parameter q-Deformed Woods-Saxon Type Potential’. The European Physical Journal Plus, vol. 133, no. 528.

Nugraha, D. A., Suparmi, A., Cari, C., & Pratiwi, B. N. (2017). ‘Asymptotic iteration method for solution of Kratzer potnetial in D-dimensional Klein-Gordon equation’. Journal of Physics: Conference Science, vol. 820, p. 1-8.

Olgar, E. & Mutaf, H. (2015). ‘Bound-State Solution of s-wave Klein-Gordon Equation for Woods-Saxon Potential’. Advances in Mathematical Physics, vol. 2015, p. 1-5.

Olgar, E, Koc, R., & Tutunculer, H. Bound states of the s-wave Klein-Gordon equation with equal scalar ad vector Standard Eckart Potential. arXiv:quant-ph/0601152v1 (2006).

Onate, C. A., Ikot, A. N., Onyeaju, M. C., & Udoh, M. E. (2017). ’Bound state solutions of D-dimensional Klein-Gordon equation with hyperbolic potential’. Karbala Int. Journal of Modern Science, vol. 3, p. 1-7.

Poojary, B. B. (2015). ‘Origin of Heisenberg’s Uncertainty Principle’. American Journal of Modern Physics. vol. 4, p. 203-211.

Soeparmi, A., Cari, C., & Elviyanti, I. L. (2018). ‘Analysis of Eigenvalue and Eigenfuntion of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential’. Journal of Physics: Conference Science, vol. 1011, p. 1-6.

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-dimensioanl harmonic oscillator potential’. Molecular Physics. vol. 118, no. 13, p. 1-10.

Suparmi, A., Permatahati, L. K., Faniandari, S.,Iriani, Y., Cari, C., & Marzuki, A. (2021). ‘Study of Bohr Mottleson Hamiltonian with minimal length effect for Woods-Saxon potential and its thermodynamic properties’. Heliyon, 7( e06861), p. 1-27.

Tezcan, C., & Sever, R. (2009). ‘A General Approach for the Exact Solution of the Schrödinger Equation’. International Journal of Theoretical Physics, vol. 48, p. 337-350.

DOI: https://doi.org/10.20961/jphystheor-appl.v5i2.55328

Refbacks

  • There are currently no refbacks.