The application bispherical coordinate in Schrödinger equation for Mobius square plus modified Yukawa potential using Nikiforov Uvarov Functional Analysis (NUFA) method

Briant Sabathino Harya Wibawa, A Suparmi, C Cari

Abstract

The application bispherical coordinates in Schrödinger equation for the Mobius square plus modified Yukawa potential have been obtained. The Schrödinger equation in bispherical coordinates for the separable Mobius square plus modified Yukawa potential consisting of the radial part and the angular part for the Mobius square plus modified Yukawa potential is solved using the variable separation method to reduce it to the radial part and angular part Schrödinger equation. The aim of this study was to solve the Schrödinger's equation of radial in bispherical coordinates for the Mobius square plus modified Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Nikiforov Uvarov Functional Analysis (NUFA) method used to obtained energy spectrum equation and wave function for the Mobius square plus modified Yukawa potential. The result of energy spectrum equation for Mobius square plus modified Yukawa potential can be shown in Equation (50). The result of un-normalized wave function equation for Mobius square plus modified Yukawa potential can be shown in Table 1.

Keywords

Schrödinger equation, bispherical coordinate, Mobius square plus modified Yukawa potential, Nikiforov Uvarov Functional Analysis (NUFA) method

Full Text:

PDF

References

Ahmadov, A. I., M. Naeem, M. V. Qocayeva, and V. A. Tarverdiyeva, (2018), “Analytical Solutions of the Schrödinger Equation for the Manning-Rosen plus Hulthén Potential Within SUSY Quantum Mechanics,” Journal of Physics: Conference Series, vol. 965, p. 012001.

Ahmadov, H. I., M. V. Qocayeva, and N. S. Huseynova, (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, vol. 26, no. 05, p. 1750028.

Arfken, G.B., H.J. Weber and F.E. Harris, (2005), Mathematical Methods for Physicists.

Bayrak O. and I. Boztosun, (2007), “Analytical solutions to the Hulthén and the Morse potentials by using the asymptotic iteration method,” Journal of Molecular Structure: THEOCHEM, vol. 802, no. 1–3, pp. 17–21.

Bayrak, O. I. Boztosun, and H. Ciftci, (2006), “Exact analytical solutions to the Kratzer potential by the asymptotic iteration method,” International Journal of Quantum Chemistry, vol. 107, no. 3, pp. 540–544.

Berkdemir C. and J. Han, (2005) “Any l-state solutions of the Morse potential through the Pekeris approximation and Nikiforov–Uvarov method,” Chemical Physics Letters, vol. 409, no. 4–6, pp. 203–207.

Edet, C. O., U. S. Okorie, A. T. Ngiangia, and A. N. Ikot, (2019), “Bound state solutions of the Schrodinger equation for the modified Kratzer potential plus screened Coulomb potential,” Indian Journal of Physics, vol. 94, no. 4, pp. 425–433.

Falaye, B. (2012), “Any ℓ-state solutions of the Eckart potential via asymptotic iteration method,” Open Physics, vol. 10, no. 4.

Gilbert P. H. and A. J. Giacomin, (2019), “Transport phenomena in bispherical coordinates,” Physics of Fluids, vol. 31, no. 2, p. 021208.

Gongora A. and K. Ley-Koo Rev, (1996), “On the evaluation of the capacitance of bispherical capacitors,” Revista Mexicana de Física 42, No. 4, 663-67.

Greene R. L. and C. Aldrich, (1976), “Variational wave functions for a screened Coulomb potential,” Physical Review A, vol. 14, no. 6, pp. 2363–2366.

Hidayat, F., A. Suparmi, and C. Cari, (2019), “Solution of Schrodinger equation in the presence of minimal length for cotangent hyperbolic potential using Hypergeometry method,” IOP Conference Series: Materials Science and Engineering, vol. 578, p. 012095.

Ikot, A. N., O. A. Awoga, and A. D. Antia, (2013), “Bound state solutions of d-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential,” Chinese Physics B, vol. 22, no. 2, p. 020304.

Majumdar, S., N. Mukherjee, and A. K. Roy, (2019), “Information entropy and complexity measure in generalized Kratzer potential,” Chemical Physics Letters, vol. 716, pp. 257–264.

Okon, I. B., O. Popoola, and C. N. Isonguyo, (2017), “Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method,” Advances in High Energy Physics, vol. 2017, pp. 1–24.

Sadeghi, J. (2007). “Factorization Method and Solution of the Non-Central Modified Kratzer Potential,” Acta Physica Polonica A, vol. 112, no. 1, pp. 23–28.

Spiegel, M. R. (1968). Mathematical Handbook of Formulas and Tables Schaum's Outline Series Schaum (Mc Graw Hill, Newyork), p. 26.

Suparmi, A. (2011). Mekanika Kuantum II, FMIPA UNS.

Suparmi, D. A. Dianawati, and Cari, (2019), “D-dimensional Klein-Gordon equation with spatially q-deformed of radial momentum for Kratzer potential analyzed by using Hypergeometric method,” Journal of Physics: Conference Series, vol. 1153, p. 012108.

Taskin F. and G. Koçak, (2010), “Approximate solutions of Schrödinger equation for Eckart potential with centrifugal term,” Chinese Physics B, vol. 19, no. 9, p. 090314.

DOI: https://doi.org/10.20961/jphystheor-appl.v4i2.42544

Refbacks

  • There are currently no refbacks.