Heavy-light mesons and diatomic molecules with improved Eckart--Hellmann potential model in a deformation space-space background: New bound states and the effect on thermodynamic properties
Keywords:
Flat plat collector, Selective coating, Optical properties, Solar irradiance.Abstract
In this research work, we investigate the 3D deformed Klien-Gordon and Schrödinger equation equations (DKGE and DSE) with the improved Eckart-Hellmann potential model (IEHP) model taking into consideration the effects of deformation space-space within the three-dimensional relativistic/non-relativistic noncommutative quantum mechanics (3D-(R/NR)NCQS) regime. The DKGE and DSE in the 3D-(R/NR) NCQS regime for this consideration are solved using the well-known Bopp's shifts method and standard perturbation theory. The new relativistic and non-relativistic energy equation and eigenfunction for the IEHP in the presence of deformation space-space for the homogeneous (I2, N2, H2) and heterogeneous (CO, NO, VH, TiH, NiC, TiC, and CuLi) diatomic molecules are obtained to be sensitive to the atomic quantum numbers ( ), the mixed potential depths ( ), the screening parameter and non-commutativity parameters. The non-relativistic limit of new energy spectra is analyzed. We examine the obtained new bound state eigenvalues of the DKGE and deformed Schrödinger equation with the IEHP in 3D-(R/NR) NCQS symmetries by suitable adjustment of the combined potential parameters and get the new modified Hellmann potential, new modified Eckart potential, new modified Coulomb potential, and new modified Yukawa potential. The homogeneous and heterogeneous composite systems under the IEHP model are investigated in the context of the 3D-NRNCQS regime. The effect of space-space deformation on the spin-averaged mass spectra of the heavy-light mesons such as (charmonium and bottomonium) under the IEHP model in 3D-NRNCQS symmetries was investigated. Furthermore, the thermal properties such as partition function, mean energy, free energy, specific heat, and entropy of the IHPMEP are duly investigated in both 3D-NRQM and 3D-NRNCQS symmetries. The present research finds many applications in various fields, such as molecular and atomic physics.
References
Hill, E.L., and Am. J. Phys. 22 (1954) 211. https://doi.org/10.1119/1.1933682
Pekeris, C.L., Phys Rev 45 (1934) 98. https://doi.org/10.1103/PhysRev.45.98
Greene, R.L., and Aldrich, C., Phys. Rev. A 14 (1976) 2363. https://doi.org/10.1103/PhysRevA.14.2363
Inyang, E., Obisung, E., William, E., and Okon, I. East European Journal of Physics, 2022 (3) (2022) 104. https://doi.org/10.26565/2312-4334-2022-3-14
Inyang, E.P., William, E.S., Omugbe, E., Inyang, E.P., Ibanga, E.A., Ayedun, F., Akpan, I.O., and Ntibi, J.E., Rev. Mex. Fís. 68 (2022) 020401. https://doi.org/10.31349/RevMexFis.68.020401
Inyang, E.P., William, E.S., Obu, J.A., Ita, B.I., Inyang, E.P., and Akpan, I.O., Molecular Physics 119(23) (2021) e1956615. https://doi.org/10.1080/00268976.2021.1956615
Eckart, C., Phys. Rev. 35 (1930) 1303. https://doi.org/10.1103/PhysRev.35.1303
Cooper, F., Khare, A., and Sukhatme, U., Physics Reports 251(5-6) (1995) 267. https://doi.org/10.1016/0370-1573(94)00080-M
Weiss, J.J., The Journal of Chemical Physics 41(4) (1964) 1120. https://doi.org/10.1063/1.1726015
Cimas, A., Aschi, M., Barrientos, C., Rayón, V.M., Sordo, J.A., and Largo, A., Chemical physics letters 374(5-6) (2003) 594. https://doi.org/10.1016/S0009-2614(03)00771-1
Diao, Y.F., Yi, L.Z., and Jia, C.S., Phys. Lett. A 332(3-4) (2004) 157. https://doi.org/10.1016/j.physleta.2004.09.051
Zou, X., Yi, L.Z., and Jia, C.S., Phys. Lett. A 346(1-3) (2005) 54. https://doi.org/10.1016/j.physleta.2005.07.075
Yahya, W.A., Oyewumi, K.J, Akoshile, C.O., Ibrahim, T.T., and Vect. J., Relativ 5 (2010) 1.
Dong, S.H., Qiang, W.C., Sun, G.H., and Bezerra, V.B., J. Phys. A: Math. Theor. 40 (34) (2007) 10535. https://doi.org/10.1088/1751-8113/40/34/010
Ikot, A.N., Maghsoodi, E., Zarrinkamar, S., et al., Few-Body Syst 55 (2014) 241. https://doi.org/10.1007/s00601-014-0862-y
Hellmann, H., The Journal of Chemical Physics 3(1) (1935) 61. https://doi.org/10.1063/1.1749559
Onate, C.A., Onyeaju, M.C., Ikot, A.N., and Ebomwonyi, O., Eur. Phys. J. Plus 132 (2017) 462. https://doi.org/10.1140/epjp/i2017-11729-8
Ikhdair, S.M., and Sever, R., Journal of Molecular Structure: THEOCHEM 809(1-3) (2007) 103. https://doi.org/10.1016/j.theochem.2007.01.019
Hall, R.L., and Katatbeh, Q.D., Physics Letters A 287(3-4) (2001) 183. https://doi.org/10.1016/S0375-9601(01)00497-2
Roy, A.K., Jalbout, A.F., and Proynov, E.I., J Math Chem 44 (2008) 260. https://doi.org/10.1007/s10910-007-9308-9
Nasser, I., and Abdelmonem, M.S., Phys. Scr. 83(5) (2011) 055004. https://doi.org/10.1088/0031-8949/83/05/055004
Hamzavi, M., Thylwe, K.E. and Rajabi, A.A., Commu. Theor. Phys. 60(1) (2013) 1. https://doi.org/10.1088/0253-6102/60/1/01
Roy, A.K, Jalbout, A.F. and Proynov, E.I., J Math Chem 44 (2008) 260. https://doi.org/10.1007/s10910-007-9308-9
M. Hamzavi, A. A. Rajabi, Canadian Journal of Physics 91(5), 411 (2013). https://doi.org/10.1139/cjp-2012-0542
Onate, C.A., Ojonubah, J.O., Adeoti, A., Eweh, J. E., and Ugboja, M.,Afr. Rev. Phys. 9(006), 497 (2014).
Douglas, M.R., and Nekrasov, N.A., Rev. Mod. Phys. 73(4) (2001) 977. https://doi.org/10.1103/RevModPhys.73.977
Moffat, J., Phys. Lett. B 493(1-2) (2000) 142. https://doi.org/10.1016/S0370-2693(00)01139-4
Connes, A., J. High Energ. Phys. 02 (1998) 003. https://doi.org/10.1088/1126-6708/1998/02/003
Hassanabadi, H., Hosseini, S.S., and Zarrinkamar, S., Int J Theor Phys. 54 (2015) 251. https://doi.org/10.1007/s10773-014-2219-1
Giri, S., Eur. Phys. J. Plus 137 (2022) 181. https://doi.org/10.1140/epjp/s13360-022-02403-5
Zeng, X.X., Eur. Phys. J. C 83 (2023) 129. https://doi.org/10.1140/epjc/s10052-023-11274-8
Trampetić, J., and You, J., Phys. Rev. D 105(7), 075016 (2022). https://doi.org/10.1103/PhysRevD.105.075016
Kan, N., Aoyama, T., Shiraishi, K., Class. Quantum Grav. 40(1) (2022) 015010. https://doi.org/10.1088/1361-6382/aca868
Rayimbaev, J., Bokhari, A.H., and Ahmedov, B., Class. Quantum Grav. 39(7), 075021 (2022). https://doi.org/10.1088/1361-6382/ac556a
Sokoliuk, O., Hassan, Z., Sahoo, P., and Baransky, A., Annals of Physics 443 (2022) 168968. https://doi.org/10.1016/j.aop.2022.168968
Gnatenko, K.P., and Tkachuk, V.M., Mod. Phys. Lett. A 31 No. 5 (2016) 1650026. https://doi.org/10.1142/S0217732316500267
Baruah, A., Goswami, P., and Deshamukhya, A., New Astronomy 99, 101956 (2023). https://doi.org/10.1016/j.newast.2022.101956
Maireche, A., Ukr. J. Phys. 67(7) (2022) 485. https://doi.org/10.15407/ujpe67.7.485
Kurkov, M., and Vitale, P., J. High Energ. Phys. 2022 (2022) 32. https://doi.org/10.1007/JHEP01(2022)032
Snyder, H.S., Phys. Rev. 71 (1947) 38. https://doi.org/10.1103/PhysRev.71.38
Connes, A., Nucl. Phys. Proc. Suppl. 18B (1991) 29. https://doi.org/10.1016/0920-5632(91)90120-4
Connes,Noncommutative Geometry (ISBN-9780121858605) 1994.
Connes, J. Math. Phys. 36 (11), 6194 (1995). https://doi.org/10.1063/1.531241
Seiberg, N., and Witten, E., J. High Energ. Phys. 1999 (09), 32 (1999). https://doi.org/10.1088/1126-6708/1999/09/032
Maireche, A., Ukr. J. Phys. 67(3) (2022) 183. https://doi.org/10.15407/ujpe67.3.183
Maireche, A., Jordan Journal of Physics 16(1) (2023) 31. https://doi.org/10.47011/16.1.4
Maireche, Few-Body Syst 63, 63 (2022). https://doi.org/10.1007/s00601-022-01766-w
Maireche, A., Int. J. Geo. Met. Mod. Phys. 19, No. 06 (2022) 2250085. https://doi.org/10.1142/S0219887822500852
Maireche, A., Rev. Mex. Fís. 68 (5) (2022) 050702 1. https://doi.org/10.31349/RevMexFis.68.050702.
Maireche, A., Rev. Mex. Fís., 68 (2) (2022.) 020801 1. https://doi.org/10. /RevMexFis.68.020801
Maireche, A., Mod. Phys. Lett. A 36(33) (2021) 2150232. https://doi.org/10.1142/S0217732321502321
Maireche, A., Ukr. J. Phys. 65(11) (2020) 987. https://doi.org/10.15407/ujpe65.11.987
Maireche, A., J Nanosci Curr Res 2 (2017) 1000115. https://doi.org/10.4172/2572-0813.1000115
Maireche, A., To Physics Journal 5, (2020) 51. http://www.purkh.com/index.php/tophy
Maireche, A., Rev. Mex. Fís. 69 (3) (2023) 030801. https://doi.org/10.31349/RevMexFis.69.030801
Terashima, S., Phys. Lett. B 482(1-3) (2000) 276. https://doi.org/10.1016/s0370-2693(00)00486-x
Maireche, A., Indian J Phys 97 (2023) 519. https://doi.org/10.1007/s12648-022-02433-w
Darroodi, M., Mehraban, H., and Hassanabadi, H., Mod. Phys. Lett. A 33 (35) (2018) 1850203. https://doi.org/10.1142/s0217732318502036
N'Dolo, E.E., Samary, D.O., Ezinvi, B., and Ounkonnou, M.N., Int. J. Geom. Met. Mod. Phys. 17(05) (2020) 2050078. https://doi.org/10.1142/s0219887820500784
Gnatenko, K.P., and Tkachuk, V.M., Int. J. Mod. Phys. A 33(07) (2018) 1850037. https://doi.org/10.1142/s0217751x18500379
Aghababaei, S., and Rezaei, G., Commun. Theor. Phys. 72 (2020) 125101. https://doi.org/10.1088/1572-9494/abb7cc
Santos, J.F.G., J. Mat. Phys. 61(12) (2020) 122101. https://doi.org/10.1063/5.0010076
Harko, T., and Liang, S.D., Eur. Phys. J. C 79(4) (2019) 300. https://doi.org/10.1140/epjc/s10052-019-6794-4
Solimanian, M., Naji, J., and Ghasemian, K., Eur. Phys. J. Plus 137 (2022) 331. https://doi.org/10.1140/epjp/s13360-022-02546-5
Oliveira, R.R.S., Alencar, G., and Landim, R.R., Gen Relativ Gravit 55 (2023) 15. https://doi.org/10.1007/s10714-022-03057-5
Kong, O.C., and Liu, W., Chin. J. Phys. 69 (2021) 70. https://doi.org/10.1016/j.cjph.2020.11.008
Mustafa, G., Hassan, Z., and Sahoo, P., Annals of Physics 437 (2022) 168751. https://doi.org/10.1016/j.aop.2021.168751
Dąbrowski, L., D'Andrea, F., and Sitarz, A., Lett Math Phys 108 (2018) 1323. https://doi.org/10.1007/s11005-017-1036-x
Gnatenko, K.P., and Shyiko, O.V., Mod. Phys. Lett. A 33(16) (2018) 1850091. https://doi.org/10.1142/S0217732318500918
Derakhshani, Z., and Ghominejad, M., Chin. J. Phys. 54(5) (2016) 761. https://doi.org/10.1016/j.cjph.2016.07.011
Chargui, Y., and Dhahbi, A., Eur. Phys. J. Plus 138 (2023) 26. https://doi.org/10.1140/epjp/s13360-023-03661-7
Wang, J., and Li, K., J. Phys. A Math. Theor. 40(9) (2007) 2197. https://doi.org/10.1088/1751-8113/40/9/021
Maireche, A., Molecular Physics (2023). https://doi.org/10.1080/00268976.2023.2205968
Maireche, A., Few-Body Syst 63 (2022) 54. https://doi.org/10.1007/s00601-022-01755-z
Maireche, A., Few-Body Syst 62 (2021) 66. https://doi.org/10.1007/s00601-021-01639-8
Maireche, A., J. Phys. Stud. 25(4) (2021) 4301. https://doi.org/10.30970/jps.25.4301
Alhaidari, D., Bahlouli, H., and Al-Hasan, A., Phys. Lett. A 349(1-4) (2006) 87. https://doi.org/10.1016/j.physleta.2005.09.008
Connes, A., J. Mat. Phys. 36(11) (1995) 6194. https://doi.org/10.1063/1.531241
Connes, A., Cuntz, J., Rieffel, M.A., and Yu, G., Oberwolfach Reports 10(3) (2013) 2553. https://doi.org/10.4171/OWR/2013/45
Ho, P. M., and Kao, H.C., Phys. Rev. Lett. 88 (15) (2002) 151602. https://doi.org/10.1103/physrevlett.88.151602
Dalabeeh, M.A., J. Phys. A: Math. Gen. 38(7) (2005) 1553. https://doi.org/10.1088/0305-4470/38/7/010
Motavalli, H., and Akbarieh, A.R., Mod. Phys. Lett. A 25(29) (2010) 2523. https://doi.org/10.1142/s0217732310033529
Mirza, M. Mohadesi, Commun. Theor. Phys. (Beijing, China) 42, 664 (2004). https://doi.org/10.1088/0253-6102/42/5/664
Bopp, F., Annales de l'institut Henri Poincaré 15 No. 2 (1956) 81.
Mezincescu, L., Star Operation in Quantum Mechanics (2000). https://arxiv.org/abs/hep-th/0007046.
Gamboa, J., Loewe, M., and Rojas, J.C., Phys. Rev. D 64 (2001) 067901. https://doi.org/10.1103/PhysRevD.64.067901
Gouba, L., Int. J. Mod. Phys. A 31(19) (2016) 1630025. https://doi.org/10.1142/s0217751x16300258
Curtright, T., Fairlie, D., and Zachos, C., Phys. Rev. D 58 (1998) 025002. https://doi.org/10.1103/PhysRevD.58.025002
Maireche, A., East European Journal of Physics 2023(1) (2023) 28. https://doi.org/10.26565/2312-4334-2023-1-03
Maireche, A., East European Journal of Physics 2022 (4) (2022) 200. https://doi.org/10.26565/2312-4334-2022-4-
Maireche, A., Bulg. J. Phys. 50(1 (2023) ) 054. https://doi.org/10.55318/bgjp.2023.50.1.054
Maireche, A., Int. J. Geom. Met. Mod. Phys. 18(13) (2021) 2150214. https://doi.org/10.1142/S0219887821502145
Maireche, A., Indian J Phys (2023). https://doi.org/10.1007/s12648-023-02681-4
Maireche, A., YJES. 19(2) (2022) 78. https://doi.org/10.53370/001c.39615
Abyaneh, M.Z. and Farhoudi, M., Eur. Phys. J. Plus 136 (2021) 863. https://doi.org/10.1140/epjp/s13360-021-01855-5
Cuzinatto, R.R., De Montigny, M., and Pompeia, P.J., Class. Quantum Grav. 39 (2022) 075007. https://doi.org/10.1088/1361-6382/ac51bc
Aounallah, H., and Boumali, A., Phys. Part. Nuclei Lett. 16 (2019) 195. https://doi.org/10.1134/S1547477119030038
Saidi, A., and Sedra, M.B., Mod. Phys. Lett. A 35(5) (2020) 2050014. https://doi.org/10.1142/s0217732320500145
Ahmadov, A., Demirci, M., Aslanova, S., and Mustamin, M., Phys. Lett. A 384(12) (2020) 126372. https://doi.org/10.1016/j.physleta.2020.126372
Tas, A., Aydogdu, O., and Salti, M., Annals of Physics 379 (2017) 67. https://doi.org/10.1016/j.aop.2017.02.010
Abramowitz, M., and Stegun, I.A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th ed., Dover Publications, Washington (1972).
Medjedel, S., and Bencheikh, K., Phys. Lett. A 383(16) (2019) 1915. https://doi.org/10.1016/j.physleta.2019.03.021
William, E.S., Inyang, E.P., and Thompson, E.A., Rev Mex Fis. 66 (2020) 730. https://doi.org/10.31349/revmexfis.66.730
Taskin, F., and Ko¸cak, G., Chin. Phys. B 19 (9) (2010) 090314. https://doi.org/10.1088/1674-1056/19/9/090314
Zhang, Y., Phys. Scr. 78(1) (2008) 015006.https://doi.org/10.1088/0031-8949/78/01/015006
Edet, O., Okorie, U. S., Ngiangia, A.T., and Ikot, A.N., Ind. J. Phys. 94 (2020) 425. https://doi.org/10.1007/s12648-019-01477-9
Onate, C.A., and Ojonubah, J.O., Int J Mod Phys E. 24 (2015) 1550.
Maireche, A., Int. J. Geom. Met. Mod. Phys. 17(5) (2020) 2050067. https://doi.org/10.1142/S021988782050067X
Maireche, A., Few-Body Syst 61 (2020) 30. https://doi.org/10.1007/s00601-020-01559-z
Maireche, A., Afr. Rev. Phys. 15 (2020) 1.
Hamzavi, M., Ikhdair, S.M., and Thylwe, K.E., Chin. Phys. B 22(4), 040301 (2013). https://doi.org/10.1088/1674-1056/22/4/040301
Maireche, A., J. Phys. Stud. 25(1) (2021) 1002. https://doi.org/10.30970/jps.25.1002
Gnatenko, K.P., Phys. Lett. A 377(43) (2013) 3061. https://doi.org/10.1016/j.physleta.2013.09.036
Abu-Shady, M., Abdel-Karim, T.A., and Ezz-Alarab, S.Y., J Egypt Math Soc 27 (2019) 14. https://doi.org/10.1186/s42787-019-0014-0
Rani, R., Bhardwaj, S.B., and Chand, F., Commun. Theor. Phys. 70 (2018) 179. https://doi.org/10.1088/0253-
Jia, S., Wang, C.W., Zhang, L.H., Peng, X.L., Zeng, R., and You, X.T., Chem. Phys. Lett. 676 (2017) 150. https://doi.org/10.10 16/j.cplett.2017.03.068
Song, X.Q., Wang, C.W., and Jia, C.S., Chem. Phys. Lett. 673 (2017) 50. https://doi.org/10.1016/j.cplett.2017.02.010
Onyenegecha, I.P., Oguzie, E.E., Njoku, I..J., Omame, A., Okereke, C.J., and Ukewuihe, U.M., Eur. Phys. J. Plus 136 (2021) 1153. https://doi.org/10.1140/epjp/s13360-021-02142-z
