EXACT SOLUTION OF THE SCHRODINGER EQUATION IN TOPOLOGICALLY MASSIVE SPACETIME

Year 2023, Volume: 6 Issue: 3-Supplement, 44 - 49, 15.10.2023

Ali Tarsuslu , Kenan Söğüt

https://doi.org/10.33773/jum.1340567

Abstract

We study exact solutions of the Schr ̈odinger equation in a topologically massive space-time. Exact solutions are obtained in terms of the hypergeometric functions. We also obtained the momentum quantization with the help of the condition of the wave function to be bounded. The investigation is performed in the framework of rainbow formalism of the General Relativity Theory (RGT). The quantized momentum is evaluated for different choices of the rainbow functions.

Keywords

Schr ̈odinger equation, exact solution, topologically massive space- time, rainbow formalism.

References

• V.M. Villalba, Separation of Variables and Exact Solution of the Klein{Gordon and Dirac Equations in an Open Universe, J. Math. Phys., Vol.43, pp.4909 (2002).
• V.M. Villalba, Particle Creation in a Cosmological Anisotropic Universe, Int. J. Theor. Phys., Vol.36, pp.1321 (1997).
• J. Audretsch, G. Schafer, Thermal particle production in a radiation dominated Robertson-Walker universe, J. Phys. A: Math. Gen., Vol.11, pp.1583 (1978).
• G. Schafer, H. Dehnen, Pair creation in cosmology when electromagnetic fields are present, J. Phys. A: Math. Gen., Vol.13, pp.517 (1980). K.H. Lotze, Production of massive spin-1/2 particles in Robertson-Walker universes with external electromagnetic fields, Astrophysics and Space Sci., Vol.120, pp.191 (1986).
• S. Biswas, Dirac equation in time dependent electric field and Robertson-Walker space-time, Pramana, Vol.36, pp.519 (1991).
• S. Haouat, R. Chekireb, Eect of electromagnetic fields on the creation of scalar particles in a at Robertson{Walker space-time, Eur. Phys. Journal C, Vol.72, 2034, (2012).
• E.E. Kangal, H. Yanar, A. Havare, K. Sogut, Creation of vector bosons by an electric field in curved spacetime, Ann. Phys., Vol.343, pp.40 (2014).
• J. Magueijo J, L. Smolin, Lorentz invariance with an invariant energy scale, Phys. Rev. Lett., Vol.88, 190403, (2002).
• J. Magueijo J, L. Smolin, Generalized Lorentz invariance with an invariant energy scale, Phys. Rev.D, Vol.67, 044017, (2003).
• J. Magueijo J, L. Smolin, Gravity's rainbow, Class. Quant. Grav., Vol.21, 1725, (2004).
• A.N., Aliev, Y. Nutku, K. Saygili, Topologically massive magnetic monopoles, Class. Quant. Grav., Vol.17, No.19, pp.4111-4123 (2000).
• Q. Exirifard, E. Karimi, Schrodinger equation in a general curved spacetime geometry, International Journal of Modern Physics D Vol. Vol.31, No.3, 2250018, (2022).
• D. Brill, J. Wheeler, Interaction of neutrinos and gravitational fields, Interaction of Neutrinos and Gravitational Fields, Rev. Mod. Phys., Vol.29, 465, (1957).
• M. Abramowitz, I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover Publications Inc., New York (1965).
• S.H. Hendi, et al., Charged dilatonic black holes in gravity's rainbow, Eur. Phys. J. C, Vol.76, 296, (2016).
• Z.W. Feng, S. Z. Yang, Thermodynamic phase transition of a black hole in rainbow gravity, Phys. Lett. B, Vol.772, No.10, pp.737-742 (2017).
• C.Z. Liu, J. Y. Zhu, Hawking radiation and black hole entropy in a gravity's rainbow, Gen. Rel. Grav., Vol.40, No.9, pp.1899-1911 (2008).
• C. Leiva, J. Saavedra, J. Villanueva, Geodesic structure of the Schwarzschild black hole in rainbow gravity, Mod. Phys. Lett. A, Vol.24, No.18, pp.1443 (2009).
• Z. Amirabi, M. Halilsoy, S. H. Mazharimousavi, Thin-shell wormholes in rainbow gravity, Mod. Phys. Lett. A, Vol.33, No.9, 1850049, (2018).