Yazar "Karayer, H." seçeneğine göre listele

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    Analytical exact solutions for the Razavy type potential
    (Wiley, 2020) Karayer, H.; Demirhan, D.; Atman, K. G.
    A quantum system with Razavy type potential which transforms to single or double well potential according to negative or positive potential parameterk, is solved analytically by using extended form of Nikiforov-Uvarov (NU) method. It is presented that eigenvalue spectra of Schrodinger equation for this potential can be attained analytically by the method. Eigenfunction solutions that are depending on confluent Heun polynomials, are analyzed graphically for specified parameters.
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    Conformable Fractional Nikiforov-Uvarov Method
    (Iop Publishing Ltd, 2016) Karayer, H.; Demirhan, D.; Buyukkihc, F.
    We introduce conformable fractional Nikiforov-Uvarov (NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schrodinger equation (SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods-Saxon potential, and Hulthen potential.
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    Extension of Nikiforov-Uvarov method for the solution of Heun equation
    (Amer Inst Physics, 2015) Karayer, H.; Demirhan, D.; Buyulkilic, F.
    We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere, and hyperbolic double-well potential are investigated by this method. (C) 2015 AIP Publishing LLC.
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    Extension of Nikiforov-Uvarov method for the solution of Heun equation
    (Amer Inst Physics, 2015) Karayer, H.; Demirhan, D.; Buyulkilic, F.
    We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere, and hyperbolic double-well potential are investigated by this method. (C) 2015 AIP Publishing LLC.
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    Extension of Nikiforov-Uvarov method for the solution of Heun equation
    (Amer Inst Physics, 2015) Karayer, H.; Demirhan, D.; Buyulkilic, F.
    We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere, and hyperbolic double-well potential are investigated by this method. (C) 2015 AIP Publishing LLC.
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    Solution of Schrodinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation
    (Amer Inst Physics, 2018) Karayer, H.; Demirhan, D.; Buyukkilic, F.
    Exact solutions of the Schrodinger equation for two different potentials are presented by using the extended Nikiforov-Uvarov method. The first one is the inverse square root potential which is a long-range potential and the second one is a combination of Coulomb, linear, and harmonic potentials which is often used to describe quarkonium. Eigenstate solutions are obtained in a systematicway without using any ansatz or transformation. Eigenfunctions for considered potentials are given in terms of biconfluent Heun polynomials. Published by AIP Publishing.
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    Solutions of local fractional sine-Gordon equations
    (Taylor & Francis Ltd, 2019) Karayer, H.; Demirhan, D.; Buyukkilic, F.
    In this paper, we study sine-Gordon equation in order to obtain exact solitary wave solutions in the domain of fractional calculus. By using the definition of conformable fractional derivative, we obtain analytical solutions of time, space and time-space fractional sine-Gordon equations. We analyze graphically the effect of fractional order on evolution of the kink and antikink type solitons.
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    SOME SPECIAL SOLUTIONS OF BICONFLUENT AND TRICONFLUENT HEUN EQUATIONS IN ELEMENTARY FUNCTIONS BY EXTENDED NIKIFOROV-UVAROV METHOD
    (Pergamon-Elsevier Science Ltd, 2015) Karayer, H.; Demirhan, D.; Buyukkilic, F.
    We report some special solutions of biconfluent Heun equation and triconfluent Heun equation via extended Nikiforov-Uvarov (NU) method which is developed by changing the boundary conditions of NU method [8]. We demonstrate that eigenvalue solutions of these confluent forms of Heun equation can be achieved exactly. Furthermore we give eigenvalue solution of a two-electron quantum dot model problem as a physical application of extended NU method.