Solutions of Schr "odinger Equation with Generalized Inverted Hyperbolic Potential (original) (raw)
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Solutions of Schrödinger Equation with Generalized Inverted Hyperbolic Potential
Journal of Modern Physics, 2012
We present the bound state solutions of the Schrödinger equation with generalized inverted hyperbolic potential using the Nikiforov-Uvarov method. We obtain the energy spectrum and the wave function with this potential for arbitrary l -state. We show that the results of this potential reduced to the standard known potentials -Rosen-Morse, Poschl Teller and Scarf potential as special cases. We also discussed the energy equation and the wave function for these special cases.
2011
We present the bound state solutions of the Schr\"odinger equation with generalized inverted hyperbolic potential using the Nikiforov-Uvarov method. We obtain the energy spectrum and the wave function with this potential for arbitrary - state. We show that the results of this potential reduced to the standard known potentials - Rosen-Morse, Poschl - Teller and Scarf potential as special cases. We also discussed the energy equation and the wave function for these special cases.
Pramana, 2012
The Nikiforov-Uvarov method is used to investigate the bound state solutions of Schrödinger equation with a generalized inverted hyperbolic potential in D-space. We obtain the energy spectrum and eigenfunction of this potential for arbitrary l-state in D dimensions. We show that the potential reduces to special cases such as Rosen-Morse, Poschl-Teller and Scarf potentials. The energy spectra and wave functions of these special cases are also discussed. The numerical results of these potentials are presented.
Bound State Solutions of the Schr\
Arxiv preprint arXiv:1012.1977, 2010
The effective mass one-dimensional Schrödinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are computed analytically. The results are also reduced to the case of constant mass. Energy eigenvalues are computed numerically for some diatomic molecules. The results are in agreement with the ones obtained before.
Studies on the Bound-State Spectrum of Hyperbolic Potential
Few-Body Systems, 2014
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary n, ℓ quantum states by solving the relevant non-relativistic Schrödinger equation allowing a nonuniform, optimal spatial discretization. Eigenvalues accurate up to tenth decimal place are reported for a large range of potential parameters; thus covering a wide range of interaction. Excellent agreement with available literature results is observed in all occasions. Special attention is paid for higher states. Some new states are given. Energy variations with respect to parameters in the potential are studied in considerable detail for the first time.
International Journal of Modern Physics E, 2008
The one-dimensional semi-relativistic equation has been solved for the [Formula: see text]-symmetric generalized Hulthén potential. The Nikiforov–Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type, is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthén potentials.
Physical Science International Journal
In this work, we applied parametric Nikiforov-Uvarov method to analytically obtained eigen solutions to Schrodinger wave equation with Trigonometric Inversely Quadratic plus Coulombic Hyperbolic Potential. We obtain energy-Eigen equation and total normalised wave function expressed in terms of Jacobi polynomial. The numerical solutions produce positive and negative bound state energies which signifies that the potential is suitable for describing both particle and anti-particle. The numerical bound state energies decreases with an increase in quantum state with fixed orbital angular quantum number 0, 1, 2 and 3. The numerical bound state energies decreases with an increase in the screening parameter and 0.5. The energy spectral diagrams show unique quantisation of the different energy levels. This potential reduces to Coulomb potential as a special case. The numerical solutions were carried out with algorithm implemented using MATLAB 8.0 software using the resulting energy-Eigen equ...
Exact and approximate solutions of Schrödinger’s equation with hyperbolic double-well potentials
European Physical Journal Plus, 2016
Analytic and approximate solutions for the energy eigenvalues generated by the hyperbolic potentials Vm(x) = −U0 sinh 2m (x/d)/ cosh 2m+2 (x/d), m = 0, 1, 2,. .. are constructed. A byproduct of this work is the construction of polynomial solutions for the confluent Heun equation along with necessary and sufficient conditions for the existence of such solutions based on the evaluation of a three-term recurrence relation. Very accurate approximate solutions for the general problem with arbitrary potential parameters are found by use of the asymptotic iteration method.