Solution of Q-Deformed D-Dimensional Klein-Gordon Equation Kratzer Potential using Hypergeometric Method
DOI:
https://doi.org/10.26740/jpfa.v9n2.p163-177Keywords:
Klein-Gordon equation, quantum deformation, Kratzer potential, Hypergeometric methodAbstract
The Q-deformed D-dimensional Klein Gordon equation with Kratzer potential is solved by using Hypergeometric method in the case of exact spin symmetry. The linear radial momentum of D-dimensional Klein Gordon equation is disturbed by the presence of the quadratic radial posisiton. The Klein-Gordon D-dimensional equation is reduced to one-dimensional Schrodinger like equation with variable substitution. The solution of the D-dimensional Klein-Gordon equation is determined in the form of a general equation of the Hypergeometry function using the Kratzer potential variable and the quantum deformation variable. From this equation, relativistic energy and wave function are determined. In addition, the relativistic energy equation can be used to calculate numerical energy levels for diatomic particles (CO, NO, O2) using Matlab R2013a software. The results obtained show that the q-deformed quantum parameters, quantum numbers and dimensions affect the value of relativistic energy for zero-pin particles. The value of energy increases with increasing value of quantum number n, q-deformed parameters, and d-dimensional parameters. Of the three parameters, q-deformed parameter is the most dominant to give change in energy value; the increasing q-deformed parameter causes the energy value increases significantly compared to the d-dimensional parameter and quantum numbers n.
References
Ita BI, Obong HP, Echi-Eromosele CO, Edobor-Osoh A, and Ikeuba AI. Solutions of the Klein-Gordon Equation with Equal Scalar and Vector Harmonic Oscillator plus Inverse Quadratic Potential. AIP Conference Proceeding. 2014; 1629(1): 162-166. DOI: https://doi.org/10.1063/1.4902270
Akaninyene DA and Ajide BA. Approximate Bound State Solution of Relativistic Klein-Gordon Particles with Physical Potentials. World Scientific News. 2018; 101: 89-107. Available from: http://psjd.icm.edu.pl/psjd/element/bwmeta1.element.psjd-4285bd46-4de1-4a4d-ac76-4df66e47d922
Laachir S and Laaribi A. Exact Solution of the Klein-Gordon Equation for the Q-Deformed Morse Potential using Nikiforov-Uvarov Method. International Journal of Recent Advances in Physics. 2014; 3(2): 49-54. DOI: https://doi.org/10.14810/ijrap.2014.3204
Nugraha DA, Suparmi A, Cari C and Pratiwi BN. Asymptotic Iteration Method for Solution of Kratzer Potential in D-Dimensional Klein-Gordon Equation. Journal of Physics Conference Series. 2017; 820: 012014. DOI: https://doi.org/10.1088/1742-6596/820/1/012014
Dehyar A, Rezaei G and Zamani A. Electronic Structure of a Spherical Quantum Dot: Effects of the Kratzer Potential, Hydrogenic Impurity, External Electric and Magnetic Fields. Physica E: Low-dimensional Systems and Nanostructures. 2016; 84: 175-181. DOI: https://doi.org/10.1016/j.physe.2016.05.038
Akpan IO, Antia AD and Ikot AN. Bound-State Solutions of the Klein-Gordon Equation with q-Deformed Equal Scalar and Vector Eckart Potential using a Newly Improved Approximation Scheme. International Scholarly Research Network High Energy Physics. 2012; 2012: 798209. DOI: http://dx.doi.org/10.5402/2012/798209
Hassanabadi H, Rahimov H and Zarrinkamar S. Approximate Solutions of Klein-Gordon Equation with Kratzer Potential. Advances in High Energy Physics. 2011; 2011: 458087. DOI: https://doi.org/10.1155/2011/458087
Suparmi. Mekanika Kuantum II. Surakarta: FMIPA UNS; 2011.
Yahya WA, Oyewumi KJ, Akoshile CO and Ibrahim TT. Bound State Solutions of the Relativistic Dirac Equation with Equal Scalar and Vector Eckart Potentials Using the Nikiforov-Uvarov Method. Journal of Vectorial Relativity. 2010; 5(3): 1-8. Available from: https://www.researchgate.net/publication/265942638_Bound_State_Solutions_of_the_Relativistic_Dirac_Equation_with_Equal_Scalar_and_Vector_Eckart_Potentials_Using_the_Nikiforov-Uvarov_Method
Cari C. Mekanika Kuantum Penyelesaian Potensial Non_sentral dengan Supersimetri, Hypergeometry, Nikifarov Uvarov dan Polynomial Romanovski. Surakarta: UNS Press; 2013.
Onate CA, Ikot AN, Onyeaju MC and Udoh ME. Bound State Solutions of D-Dimensional Klein-Gordon Equation with Hyperbolic Potential. Karbala International Journal of Modern Science. 2017; 3(1): 1-7. DOI: https://doi.org/10.1016/j.kijoms.2016.12.001
Chabab M, Lahbas A and Oulne M. 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 Potentials. International Journal of Modern Physics E. 2012; 21(10): 1250087. DOI: https://doi.org/10.1142/S0218301312500875
Bayrak O, Boztosun I and Ciftci H. Exact Analytical Solutions to the Kratzer Potential by the Asymptotic Iteration Method. International Journal of Quantum Chemistry. 2006; 107(3): 540-544. DOI: https://doi.org/10.1002/qua.21141
Majumdar S, Mukherjee N and Roy AK. Information Entropy and Complexity Measure in Generalized Kratzer Potential. Chemical Physics Letters. 2019; 716: 257-264. DOI: https://doi.org/10.1016/j.cplett.2018.12.032
Hoseini F, Saha JK and Hassanabadi H. Investigation of Fermions in Non-Commutative Space by Considering Kratzer Potential. Communications in Theoritical Physics. 2016; 65(6): 695-700. DOI: https://doi.org/10.1088/0253-6102/65/6/695
Bao J and Shizgal BD. Pseudospectral Method of Solution of the Schrodinger Equation for the Kratzer and Pseudoharmonic Potentials with Nonclassical Polynomials and Applications to Realistic Diatom Potentials. Computational and Theoretical Chemistry. 2019; 1149: 49-56. DOI: https://doi.org/10.1016/j.comptc.2019.01.001
Sobhani H, Chung WS and Hassanabadi H. Investigation of Spin-Zero Bossons in Q-Deformed Relativistic Quantum Mechanics. Indian Journal of Physics. 2017; 92(4): 529-536. DOI: https://doi.org/10.1007/s12648-017-1121-0
Suparmi A, Cari C, and Yuliani H. 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. DOI: https://doi.org/10.7176/APTA-16-8.
Sargolzaeipor S, Hassanabadi H and Chung WS. Q-Deformed Superstatistics of the Schrodinger Equation in Commutative and Noncommutative Spaces with Magnetic Field. The European Physics Journal Plus. 2018; 133: 5. DOI: https://doi.org/10.1140/epjp/i2018-11827-1
Dong SH. Wave Equations in Higher Dimensions. Netherlands: Springer; 2011. DOI: https://doi.org/10.1007/978-94-007-1917-0
Dong SH. The Ansatz Method for Analyzing Schrodingers Equation with Thee Anharmonic Potentials in D Dimension. Journal of Genetic Counseling. 2002; 15(4): 385-395. DOI: https://doi.org/10.1023/A:1021220712636
Widiyanto F, Suparmi A, Cari X, Anwar F, and Yunianyo M. Schrodinger Equation Solution for Q-Deformed Scarf II Potential plus Poschl-Teller Potential and Trigonometric Scarf Potential. Journal of Physics: Conference Series. 2017; 909: 012036. DOI: https://doi.org/10.1088/1742-6596/909/1/012036
Suparmi A, Cari C, Pratiwi BN and Deta UA. Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties. AIP Conference Proceedings. 2016; 1710: 030010. DOI: https://doi.org/10.1063/1.4941476
Ikot AN, Anita AD, Akpan IO and Awoga OA. Bound State Solutions of Schrodinger Equation with Modified hylleraas plus Exponential Rosen Morse Potential. Revista Mexicana de Fisica. 2013; 59: 46-53. Available from: https://rmf.smf.mx/pdf/rmf/59/1/59_1_46.pdf.
Hassanabadi H, Chung WS, Zare S and Bhardwaj SB. Q-Deformed Morse and Oscillator Potential. Advances in High Energy Physics. 2017; 2017: 1730834. DOI: https://doi.org/10.1155/2017/1730834
Ikot AN, Hassanabadi H, Obong HP, Chad Umoren YE, Isonguyo CN and Yazarloo BH. Approximate Solution of Klein-Gordon Equation with Improved Manning-Rosen Potential in D-Dimensions using SUSYQM. Chinese Physics B. 2014; 23(12): 120303. DOI: https://doi.org/10.1088/1674-1056/23/12/120303
Curado EMF and Tsallis C. Generalized Statistical Mechanics: Connection with Thermodynamics. Journal of Physics A: Mathematical and General. 1991; 24(2): L69. DOI: https://doi.org/10.1088/0305-4470/24/2/004
Tsallis C. Possible Generalization of Boltzmann-Gibbs Statistics. Journal of Statistical Physics. 1988; 52(1-2): 479-487. DOI: https://doi.org/10.1007/BF01016429
Jang EJ, Cha J, Lee YK and Chung WS. On the q-Tunable quantum Mechanics Based on the Tsallis Entropy Formula. Advanced Studies in Theoretical Physics. 2016; 10(3): 99-112. DOI: https://doi.org/10.12988/astp.2016.512112
Suyari H. Mathematical Structures Derived from the Q-Multinomial Coefficient in Tsallis Statistics. Physics A: Statistical Mechanics and Its Application. 2006; 368(1): 63-82. DOI: https://doi.org/10.1016/j.physa.2005.12.061
Abe S and Okamoto Y. Nonextensive Statistical Mechanics and Its Applications. Heidelberg: Springer-Verlag; 2001.
Borges EP. A Possible Deformed Algebra and Calculus inspired in Nonextensive Thermostatistics. Physics A: Statistical Mechanics and Its Application. 2004; 340(1-3): 95-101. DOI: https://doi.org/10.1016/j.physa.2004.03.082
Suyari H. Generalization of Shannon-Khinchin Axioms to Nonextensive Systems and the Uniqueness Theorem for the Nonextensive entropy. IEEE Transactions on Information Theory. 2004; 50(8): 1783-1787. DOI: https://doi.org/10.1109/TIT.2004.831749
'
Sobhani H, Chung WS and Hassanabadi H. Q-Deformed Relativistic Fermion Scattering. Advances in High Energy Physics. 2017; 2017: 9530874. DOI: https://doi.org/10.1155/2017/9530874
Saad N, Hall RL and Ciftci H. The Klein-Gordon Equation with the Kratzer Potential. Central European Journal of Physics. 2008; 6(3): 717-729. DOI: https://doi.org/10.2478/s11534-008-0022-4
Darrodi M, Mehraban H and Hassanabadi S. The Klein-Gordon Equation with the Kratzer Potential in the Noncommutative Space. Modern Physics Letters A. 2018; 33(35): 1850203. DOI: https://doi.org/10.1142/S0217732318502036
Nugraha DA, Suparmi A, Cari C and Pratiwi BN. Asymptotic Iteration Method for Analytical Solution of Klein-Gordon Equation for Trigonometric Poschl-Teller Potential in D-Dimensions. Journal of Physics Conference Series. 2017; 795: 012025. DOI: https://doi.org/10.1088/1742-6596/795/1/012025
R Nishimura. Monotonicity of Asymptotic Relations for Generalized Hypergeometric Functions. Journal of Mathematical Analysis and Applications. 2019. DOI: https://doi.org/10.1016/j.jmaa.2019.123377
Dianawati DA, Suparmi A and Cari C. Solution of Schrodinger Equation with Q-Deformed Momentum in Coulomb Potential Using Hypergeometric Method. AIP Conference Proceedings. 2018; 2014: 020071. DOI: https://doi.org/10.1063/1.5054475
Akaninyene DA and Ajide BA. Approximate Bound State Solution of Relativistic Klein-Gordon Particles with Physical Potentials. World Scientific News. 2018; 101: 89-107. Available from: http://psjd.icm.edu.pl/psjd/element/bwmeta1.element.psjd-4285bd46-4de1-4a4d-ac76-4df66e47d922
Laachir S and Laaribi A. Exact Solution of the Klein-Gordon Equation for the Q-Deformed Morse Potential using Nikiforov-Uvarov Method. International Journal of Recent Advances in Physics. 2014; 3(2): 49-54. DOI: https://doi.org/10.14810/ijrap.2014.3204
Nugraha DA, Suparmi A, Cari C and Pratiwi BN. Asymptotic Iteration Method for Solution of Kratzer Potential in D-Dimensional Klein-Gordon Equation. Journal of Physics Conference Series. 2017; 820: 012014. DOI: https://doi.org/10.1088/1742-6596/820/1/012014
Dehyar A, Rezaei G and Zamani A. Electronic Structure of a Spherical Quantum Dot: Effects of the Kratzer Potential, Hydrogenic Impurity, External Electric and Magnetic Fields. Physica E: Low-dimensional Systems and Nanostructures. 2016; 84: 175-181. DOI: https://doi.org/10.1016/j.physe.2016.05.038
Akpan IO, Antia AD and Ikot AN. Bound-State Solutions of the Klein-Gordon Equation with q-Deformed Equal Scalar and Vector Eckart Potential using a Newly Improved Approximation Scheme. International Scholarly Research Network High Energy Physics. 2012; 2012: 798209. DOI: http://dx.doi.org/10.5402/2012/798209
Hassanabadi H, Rahimov H and Zarrinkamar S. Approximate Solutions of Klein-Gordon Equation with Kratzer Potential. Advances in High Energy Physics. 2011; 2011: 458087. DOI: https://doi.org/10.1155/2011/458087
Suparmi. Mekanika Kuantum II. Surakarta: FMIPA UNS; 2011.
Yahya WA, Oyewumi KJ, Akoshile CO and Ibrahim TT. Bound State Solutions of the Relativistic Dirac Equation with Equal Scalar and Vector Eckart Potentials Using the Nikiforov-Uvarov Method. Journal of Vectorial Relativity. 2010; 5(3): 1-8. Available from: https://www.researchgate.net/publication/265942638_Bound_State_Solutions_of_the_Relativistic_Dirac_Equation_with_Equal_Scalar_and_Vector_Eckart_Potentials_Using_the_Nikiforov-Uvarov_Method
Cari C. Mekanika Kuantum Penyelesaian Potensial Non_sentral dengan Supersimetri, Hypergeometry, Nikifarov Uvarov dan Polynomial Romanovski. Surakarta: UNS Press; 2013.
Onate CA, Ikot AN, Onyeaju MC and Udoh ME. Bound State Solutions of D-Dimensional Klein-Gordon Equation with Hyperbolic Potential. Karbala International Journal of Modern Science. 2017; 3(1): 1-7. DOI: https://doi.org/10.1016/j.kijoms.2016.12.001
Chabab M, Lahbas A and Oulne M. 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 Potentials. International Journal of Modern Physics E. 2012; 21(10): 1250087. DOI: https://doi.org/10.1142/S0218301312500875
Bayrak O, Boztosun I and Ciftci H. Exact Analytical Solutions to the Kratzer Potential by the Asymptotic Iteration Method. International Journal of Quantum Chemistry. 2006; 107(3): 540-544. DOI: https://doi.org/10.1002/qua.21141
Majumdar S, Mukherjee N and Roy AK. Information Entropy and Complexity Measure in Generalized Kratzer Potential. Chemical Physics Letters. 2019; 716: 257-264. DOI: https://doi.org/10.1016/j.cplett.2018.12.032
Hoseini F, Saha JK and Hassanabadi H. Investigation of Fermions in Non-Commutative Space by Considering Kratzer Potential. Communications in Theoritical Physics. 2016; 65(6): 695-700. DOI: https://doi.org/10.1088/0253-6102/65/6/695
Bao J and Shizgal BD. Pseudospectral Method of Solution of the Schrodinger Equation for the Kratzer and Pseudoharmonic Potentials with Nonclassical Polynomials and Applications to Realistic Diatom Potentials. Computational and Theoretical Chemistry. 2019; 1149: 49-56. DOI: https://doi.org/10.1016/j.comptc.2019.01.001
Sobhani H, Chung WS and Hassanabadi H. Investigation of Spin-Zero Bossons in Q-Deformed Relativistic Quantum Mechanics. Indian Journal of Physics. 2017; 92(4): 529-536. DOI: https://doi.org/10.1007/s12648-017-1121-0
Suparmi A, Cari C, and Yuliani H. 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. DOI: https://doi.org/10.7176/APTA-16-8.
Sargolzaeipor S, Hassanabadi H and Chung WS. Q-Deformed Superstatistics of the Schrodinger Equation in Commutative and Noncommutative Spaces with Magnetic Field. The European Physics Journal Plus. 2018; 133: 5. DOI: https://doi.org/10.1140/epjp/i2018-11827-1
Dong SH. Wave Equations in Higher Dimensions. Netherlands: Springer; 2011. DOI: https://doi.org/10.1007/978-94-007-1917-0
Dong SH. The Ansatz Method for Analyzing Schrodingers Equation with Thee Anharmonic Potentials in D Dimension. Journal of Genetic Counseling. 2002; 15(4): 385-395. DOI: https://doi.org/10.1023/A:1021220712636
Widiyanto F, Suparmi A, Cari X, Anwar F, and Yunianyo M. Schrodinger Equation Solution for Q-Deformed Scarf II Potential plus Poschl-Teller Potential and Trigonometric Scarf Potential. Journal of Physics: Conference Series. 2017; 909: 012036. DOI: https://doi.org/10.1088/1742-6596/909/1/012036
Suparmi A, Cari C, Pratiwi BN and Deta UA. Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties. AIP Conference Proceedings. 2016; 1710: 030010. DOI: https://doi.org/10.1063/1.4941476
Ikot AN, Anita AD, Akpan IO and Awoga OA. Bound State Solutions of Schrodinger Equation with Modified hylleraas plus Exponential Rosen Morse Potential. Revista Mexicana de Fisica. 2013; 59: 46-53. Available from: https://rmf.smf.mx/pdf/rmf/59/1/59_1_46.pdf.
Hassanabadi H, Chung WS, Zare S and Bhardwaj SB. Q-Deformed Morse and Oscillator Potential. Advances in High Energy Physics. 2017; 2017: 1730834. DOI: https://doi.org/10.1155/2017/1730834
Ikot AN, Hassanabadi H, Obong HP, Chad Umoren YE, Isonguyo CN and Yazarloo BH. Approximate Solution of Klein-Gordon Equation with Improved Manning-Rosen Potential in D-Dimensions using SUSYQM. Chinese Physics B. 2014; 23(12): 120303. DOI: https://doi.org/10.1088/1674-1056/23/12/120303
Curado EMF and Tsallis C. Generalized Statistical Mechanics: Connection with Thermodynamics. Journal of Physics A: Mathematical and General. 1991; 24(2): L69. DOI: https://doi.org/10.1088/0305-4470/24/2/004
Tsallis C. Possible Generalization of Boltzmann-Gibbs Statistics. Journal of Statistical Physics. 1988; 52(1-2): 479-487. DOI: https://doi.org/10.1007/BF01016429
Jang EJ, Cha J, Lee YK and Chung WS. On the q-Tunable quantum Mechanics Based on the Tsallis Entropy Formula. Advanced Studies in Theoretical Physics. 2016; 10(3): 99-112. DOI: https://doi.org/10.12988/astp.2016.512112
Suyari H. Mathematical Structures Derived from the Q-Multinomial Coefficient in Tsallis Statistics. Physics A: Statistical Mechanics and Its Application. 2006; 368(1): 63-82. DOI: https://doi.org/10.1016/j.physa.2005.12.061
Abe S and Okamoto Y. Nonextensive Statistical Mechanics and Its Applications. Heidelberg: Springer-Verlag; 2001.
Borges EP. A Possible Deformed Algebra and Calculus inspired in Nonextensive Thermostatistics. Physics A: Statistical Mechanics and Its Application. 2004; 340(1-3): 95-101. DOI: https://doi.org/10.1016/j.physa.2004.03.082
Suyari H. Generalization of Shannon-Khinchin Axioms to Nonextensive Systems and the Uniqueness Theorem for the Nonextensive entropy. IEEE Transactions on Information Theory. 2004; 50(8): 1783-1787. DOI: https://doi.org/10.1109/TIT.2004.831749
'
Sobhani H, Chung WS and Hassanabadi H. Q-Deformed Relativistic Fermion Scattering. Advances in High Energy Physics. 2017; 2017: 9530874. DOI: https://doi.org/10.1155/2017/9530874
Saad N, Hall RL and Ciftci H. The Klein-Gordon Equation with the Kratzer Potential. Central European Journal of Physics. 2008; 6(3): 717-729. DOI: https://doi.org/10.2478/s11534-008-0022-4
Darrodi M, Mehraban H and Hassanabadi S. The Klein-Gordon Equation with the Kratzer Potential in the Noncommutative Space. Modern Physics Letters A. 2018; 33(35): 1850203. DOI: https://doi.org/10.1142/S0217732318502036
Nugraha DA, Suparmi A, Cari C and Pratiwi BN. Asymptotic Iteration Method for Analytical Solution of Klein-Gordon Equation for Trigonometric Poschl-Teller Potential in D-Dimensions. Journal of Physics Conference Series. 2017; 795: 012025. DOI: https://doi.org/10.1088/1742-6596/795/1/012025
R Nishimura. Monotonicity of Asymptotic Relations for Generalized Hypergeometric Functions. Journal of Mathematical Analysis and Applications. 2019. DOI: https://doi.org/10.1016/j.jmaa.2019.123377
Dianawati DA, Suparmi A and Cari C. Solution of Schrodinger Equation with Q-Deformed Momentum in Coulomb Potential Using Hypergeometric Method. AIP Conference Proceedings. 2018; 2014: 020071. DOI: https://doi.org/10.1063/1.5054475
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2019-12-31
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Suparmi, S., Dianawati, D. A. and Cari, C. (2019) “Solution of Q-Deformed D-Dimensional Klein-Gordon Equation Kratzer Potential using Hypergeometric Method”, Jurnal Penelitian Fisika dan Aplikasinya (JPFA), 9(2), pp. 163–177. doi: 10.26740/jpfa.v9n2.p163-177.
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