Analytical Solutions of Schrödinger Equation with Two- Dimensional Harmonic Potential in Cartesian and Polar Coordinates Via Nikiforov-Uvarov Method (original) (raw)
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In this paper, we have solved the Schrodinger equation with a new superposed potential (IQYARP) made of inversely quadratic Yukawa potential and attractive radial potential using the parametric Nikiforov-Uvarov (NU) method. The solutions of the Schrodinger equation enabled us to obtainbound state energy eigenvalues and their corresponding un-normalized eigen functions in terms of Jacobi polynomials. Also, a special case of the potential has been considered and its energy eigen values obtained. Our calculation reveals bound state energy eigenvalues which can be applied to molecules moving under the influence of IQYARP potential.
It is well known that the exact solutions play an important role in quantum mechanics since they contain all the necessary information regarding the quantum model under study. However, the exact analytic solutions of nonrelativistic and relativistic wave equations are only possible for certain potentials of physical interest. In this paper, bound state solutions of the Schrodinger and Klein-Gordon equations with Modified Hylleraas plus attractive radial potentials (MHARP), have been obtained using the parametric Nikiforov-Uvarov (NU) method which is based on the solutions of general second-order linear differential equations with special functions. The bound state eigen energy solutions for both wave equations were obtained. Also special cases of the potential have been considered and their energy eigen values obtained. Abstract-It is well known that the exact solutions play an important role in quantum mechanics since they contain all the necessary information regarding the quantum model under study. However, the exact analytic solutions of nonrelativistic and relativistic wave equations are only possible for certain potentials of physical interest. In this paper, bound state solutions of the Schrodinger and Klein-Gordon equations with Modified Hylleraas plus attractive radial potentials (MHARP), have been obtained using the parametric Nikiforov-Uvarov (NU) method which is based on the solutions of general second-order linear differential equations with special functions. The bound state eigen energy solutions for both wave equations were obtained. Also special cases of the potential have been considered and their energy eigen values obtained.
gazi university journal of science, 2016
In this paper, we studied the Schrödinger equation with the generalized Hulthen potential plus a new ring shaped potential. We obtained approximately the bound state energy spectra and the corresponding wave function using the functional analysis method. We used the well-known Hellmann-Feynmann theorem to calculate the expectation values for 12 1 , 1 rr ee 12 , rr , 2 cot , 2 tan and 22 cos sec ec .We also discussed the special case of the potential which was consistent with the results found in the literature.
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An approximate solution of the Schrödinger equation for the generalized Hulthén potential with non-zero angular quantum number is solved. The bound state energy eigenvalues and eigenfunctions are obtained in terms of Jacobi polynomials. The Nikiforov-Uvarov method is used in the computations. We have considered the timeindependent Schrödinger equation with the associated form of Hulthén potential which simulate the effect of the centrifugal barrier for any l-state. The energy levels of the used Hulthén potential gives satisfactory values for the non-zero angular momentum as the generalized Hulthén effective potential.
abstract An exact analytical and approximate solution of the relativistic and non-relativistic wave equations for central potentials has attracted enormous interest in recent years. By using the basic Nikiforov-Uvarov quantum mechanical concepts and formalism, the energy eigenvalue equations and the corresponding wave functions of the Klein–Gordon and Schrodinger equations with the interaction of Modified Hylleraas-Hulthen Potentials (MHHP) were obtained using the conventional Pekeris-type approximation scheme to the orbital centrifugal term.The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials. article History introduction Quantum mechanical Wavefunctions and their corresponding eigenvalues give significant information in describing various quantum systems 1-3. Bound state solutions of relativistic and nonrelativistic wave equation arouse a lot of interest for decades.
Any l -state solutions of the Hulthén potential by the asymptotic iteration method
Journal of Physics A: Mathematical and General, 2006
In this article, we present the analytical solution of the radial Schrödinger equation for the Hulthén potential within the framework of the asymptotic iteration method by using an approximation to the centrifugal potential for any l states. We obtain the energy eigenvalues and the corresponding eigenfunctions for different screening parameters. The wave functions are physical and energy eigenvalues are in good agreement with the results obtained by other methods for different δ values. In order to demonstrate this, the results of the asymptotic iteration method are compared with the results of the supersymmetry, the numerical integration, the variational and the shifted 1/N expansion methods.
2007
We present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for an alternative (often used) pseudo-Coulomb potential-plus- ring-shaped potential of the form V(r)=−V(r)=-% \frac{a}{r}+\frac{b}{r^{2}}+\frac{\beta \cos ^{2}\theta}{r^{2}\sin ^{2}\theta }+cV(r)=− by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the radial and angular parts of the wave functions in terms of orthogonal polynomials. The total energy of the system is different from the pseudo-Coulomb potential because of the contribution of the angular part. The general results obtained in this work can be reduced to the standard forms given in literature.