The aims of the research are to determine energy spectra and radial wave function of Quantum system in D-Dimensions for Eckart plus Manning Rosen potential with Nikiforov-Uvarov method. NikiforovUvarov method is method for solving a second-order of differential equations by transforming the equation into the hypergeometric equation by the method of separation of intermediate variables by appropriate variable substitution. The analytical results is energy spectra and radial wave function visualization by Microsoft Excel 2010 and Mathematical Laboratory 2013 Programing. The visualization result can be showed that the orbital quantum number increase and the dimension increase causing the bounding energy decrease in the –n spectra energy. The probability visualization for ground state condition result can be showed that the orbital increase, so probability decrease, while the dimension increase for ground state condition is decreasing probability.
The aims of the research are to determine energy spectra and radial wave function of Quantum system in D-Dimensions for Eckart plus Manning Rosen potential with Nikiforov-Uvarov method. NikiforovUvarov method is method for solving a second-order of differential equations by transforming the equation into the hypergeometric equation by the method of separation of intermediate variables by appropriate variable substitution. The analytical results is energy spectra and radial wave function visualization by Microsoft Excel 2010 and Mathematical Laboratory 2013 Programing. The visualization result can be showed that the orbital quantum number increase and the dimension increase causing the bounding energy decrease in the –n spectra energy. The probability visualization for ground state condition result can be showed that the orbital increase, so probability decrease, while the dimension increase for ground state condition is decreasing probability.
This research’s aim are to determine energy spectra and wave function of
Schrodinger Equation in D-Dimensions for non central shape invariant potentials,
that is, Scarf hyperbolic plus non central Poschl-Teller potential and Scarf
trigonometric plus non central Rosen-Morse potential with Nikivarof-Uvarov
method. Nikivarof-Uvarov method are the method for solving a second order of
differential equation which transform that equation into hypergeometric equation
using a correct subtitution of variable.
Research was done through a literature studies to solve the Schrodinger
equation D-Dimensions analitically for Scarf hyperbolic plus non central Poschl-
Teller potential and Scarf trigonometric plus non central Rosen-Morse potential.
Energy spectra and wave function obtained by Nikivarof-Uvarov method. After
obtaining energy levels and compared with the other methods in the special
conditions, the wave function can be obtained by Nikivarof-Uvarov method.
Energy spectra of the Scarf hyperbolic plus non-central Poschl Teller
potential and Scarf trigonometric plus non-central Rosen Morse potential on DDimensions
which obtained by Nikiforov-Uvarof methods have a results
consistently with previous research on special condition. Energy spectra and wave
functions of both combination of potentials are determined approximately for the
value of orbital quantum number l ≠ 0.
Keywords: Schrodinger Equation in D-Dimensions, Non Central Shape Invariant
Potentials, and Nikivarof-Uvarov Method.
The exact solutions of the Schrodinger equations (SE) in the D-dimensional coordinate system have attracted the attention of many theoretical researchers in branches of quantum physics and quantum chemistry. The energy eigenvalues and the wave function are the solutions of the Schrodinger equation that implicitly represents the behavior of a quantum mechanical system. This study aimed to obtain the eigenvalues, wave functions, and thermodynamic properties of the 6-Dimensional Schrodinger equation under Double Ring-Shaped Oscillator (DRSO) and Manning-Rosen potential. The variable separation method was applied to reduce the one 6-Dimensional Schrodinger equation depending on radial and angular non-central potential into five onedimensional Schrodinger equations: one radial and five angular Schrodinger equations. Each of these onedimensional Schrodinger equations was solved using the SUSY QM method to obtain one eigenvalue and one wave function of the radial part, five eigenvalues, and five angular wave functions angular part. Some thermodynamic properties such, the vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆, were obtained using the radial energy equations. The results showed that except the 𝑛𝑙1, all increment of angular quantum number decreases the energy values. Increments of all potential parameter increase the energy values. Increment of angular quantum number and potentials parameter increases the amplitude and shifts the wave functions to the left. However, the increment of 𝑛𝑙1, 𝛼, 𝜎, and 𝜌 decrease the amplitude and shift wavefunctions to the right. Moreover, the vibrational mean energy 𝑈 and free energy 𝐹 increased as the increasing value of potentials parameters, where the ω parameter has the dominant effect than the other parameters. The vibrational specific heat 𝐶 and entropy 𝑆 affected only by the 𝜔 parameter, where 𝐶 and 𝑆 decreased as the increase of 𝜔.
The purposes of the research were to determine the energy spectrum and
wave function of some q-deformed non-central shape invariance potentials,
Modified Poschl-Teller plus Scarf potential and Rosen-Morse plus Rosen-Morse
potential using Nikiforov-Uvarov Method.
The research was a literature study to solve Schrodinger equation for qdeformed
Modified Poschl-Teller plus Scarf potential and Rosen-Morse plus
Rosen-Morse potential analytically. The energy spectrum and the wave functions
of a system particles can be determined by Schrodinger equation. The energy
spectrum and wave function for q-deformed non-central potential determined by
Nikiforov-Uvarov method. Generally, the Schrodinger equation for the noncentral
potential can be solved by exact if the potential variables separated into
the radial and angular part. The energy spectrum and the radial wave function
obtained approximately due to the centrifugal term from the radial Schrodinger
equation, while the angular wave function and the orbital quantum number are
obtained from angular part of Schrodinger equation.
Key words: The Energy Spectrum, Wave Function, Schrodinger Equation, Non-
Central, q-deformed, Nikiforov-Uvarov Method.
Background: The analytical solution of the Schrödinger equation in bispherical coordinates has attracted a great deal of interest for theoretical physics researchers in the branch of quantum physics. The energy and wave function are solutions of the Schrödinger equation which are very important because it contains all necessary information regarding the behavior of quantum systems. Aim: This study aimed to obtain energy, radial wave functions and thermodynamic properties for diatomic molecules from the radial part of the Schrödinger equation in bispherical coordinates for the modified Mobius square plus Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Methods: The variable separation method was applied to reduce the Schrodinger equation in bispherical coordinates to the radial part and angular part Schrodinger equation. The Schrodinger equation of the radial part in bispherical coordinates was solved using the Nikiforov Uvarov Functional Analysis (NUFA) method to obtain the energy equation and radial wave function. Furthermore, the vibrational partition function 𝑍 was obtained from the energy equation. The vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆 were obtained from the vibrational partition function 𝑍. Results and Discussion: The results showed that the increase of parameters of 𝑛 and 𝛼 caused the decrease of energy, but the increase of parameters of 𝐿 and 𝑚0 caused the increase of energy. The radial quantum number 𝑛 and the potential range 𝛼 had the most effect to the wave functions. The parameters 𝑛𝑚𝑎𝑥, 𝑇, and 𝛼 had effect to the vibrational partition function 𝑍, vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆. Conclusions: From the results of this study, it can be concluded that the energy, radial wave function, and thermodynamic properties for diatomic molecules have been obtained using the Nikiforov Uvarov Functional Analysis (NUFA) method.
In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.
In this paper, the bound state solution of the modified radial Schrödinger equation is obtained for the Manning-Rosen plus Hulthén potential by implementing the novel improved scheme to surmount the centrifugal term. The energy eigenvalues and corresponding radial wave functions are defined for any l ≠ 0 angular momentum case via the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods. By using these two different methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary l states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.