Introduction over the past couple of decades, new algoritms have improved the accuracy. We obtain the energy eigenvalues and the corresponding eigenfunctions for any arbitrary lstate using the parametric nikiforovuvarov method. Pdf solutions for a generalized woodssaxon potential. Single particle calculations for a woodssaxon potential. Solutions of ddimensional schrodinger equation for woodssaxon. The woods saxon potential is probably the most studied and widely used short range potential in all of nuclear physics. The energy eigenvalues are reported and the corresponding wave functions are calculated in terms of hypergeometric functions. In fact, this particular case will cover most of the problems that well encounter in ee 439. Akpabio and akaninyene d antia 2011 exactsolutions of schrodinger equation with woods saxon plus rosenmorse potential. Ahmador, analytical solution of the schrodinger equation withthe woods saxon potential for arbitrary l state, arxiv. The dirac equation, which describes the motion of a spin 12 particle, has been. The woods saxon potential plays an important role in microscopic physics, since it can be used to describe the interaction of a nucleon with the heavy nucleus. Because our approach makes the most of newtons method in this paper, our calculations.
Solution of the schrodinger equation including the above potentials has been done by the numerical methods in the abovementioned works. The effectivemass schrodinger equation could be transformed into heuns equation which is a fuchsiantype equation with four singularities by using a coordinate transformation. R c spherical nucleus radius and solution of the schrodinger equation by nikiforov. We also obtained the energy eigen value and its associated total wave function. R0 a,a single particle calculations for a woods saxon cartesian. Generalized nuclear woodssaxon potential under relativistic spin. Solutions of the central woodssaxon potential in l 0 case using. However, unlike newtons laws, the schrodinger equation does not give the trajectory of a particle, but rather the wave function of the quantum system, which carries information about the wave nature of. Pdf scattering of woodssaxon potential in schrodinger.
Exact bound state solution of qdeformed woodssaxon plus. They did not include the coulomb term to their calculations. While it is possible to solve the schr odinger equation for this potential, it is not trivial. New elegant approximation method is used to deal with the centrifugal term. Nuclear and particle physics lecture 20 the shell model. The swave schrodinger and, to clarify one interesting point encountered in the calculations, kleingordon equations are solved exactly for a single neutron. Lecture 3 solving the nonrelativistic schroedinger equation. Pdf the scattering solutions of the onedimensional schrodinger equation for the woods saxon potential are obtained within the positiondependent mass. The woodssaxonlike potential characterized by a rapid increase occurred at the systems boundary varies slowly inside and quickly becomes a constant potential outside the system.
Pdf scattering of woodssaxon potential in schrodinger equation. In 1 dimension 2, if you count time, the equation of motion of a mass with kinetic energy k, under the in. But the modified woodssaxon potential has no exact or approximate. The schr odinger equation with the woodssaxon potential is considered for an sstate. Nuclear physics, energy levels, wave functions, schrodinger equation, woods saxon potential nature of the problem. We study the ddimensional kleingordon equation for the modified hylleraas potential with position dependent mass. We obtain the wavefunction in terms of heuns function and then we find transmission. Schrodinger equation, angular momentum, woodssaxon potential, bound states, special functions. Solutions of ddimensional schrodinger equation for woods. Single particle calculations for a woodssaxon potential with triaxial deformations, and large cartesian oscillator basis triaxial 2014, third version of the code triaxial. Scattering of the woodssaxon potential in the schrodinger. Woodsaxon potential or finite square well is used in nuclear orbit. Analytical solutions of the schr\o dinger equation with the woods.
Debnath2 1tansuk rai ganapat rai khemka high school, 23, rabindra sarani, liluah, howrah711204, india 2department of mathematics, jadavpur university, kolkata700032, india received 26 march 2009. Calculation of the eigenvalues for woodsaxons potential. Solaimani 0 1 0 department of physics, faculty of science, qom university of technology, qom, iran 1 physics faculty, shahrood university, p. One solution is obtained analytically by means of the. Another one is obtained numerically using the rungekutta method. Pdf the scattering solutions of the onedimensional schrodinger equation for the woodssaxon potential are obtained within the positiondependent mass. In the framework of the ptsymmetric quantum mechanics, we secondly solved the timeindependent schrodinger equation for. Communications in theoretical physics nuclear physics.
The woods saxon potential is a mean field potential for the nucleons protons and neutrons inside the atomic nucleus, which is used to describe approximately the forces applied on each nucleon, in the nuclear shell model for the structure of the nucleus. Schrodinger equation stationary states in fact all possible solutions to the schrodinger equation can be written in this way. In this work, we obtained an exact solution to schrodinger equation using qdeformed woodssaxon plus modified coulomb potential using conventional nikiforovuvarov method. Pdf newton s method and energy eigenvalue problems for.
Pahlavani 27 formulated an hierarchy of hamiltonian for spherical woodssaxon potential the qdeformed woodssaxon plus modified coulomb potential is given by 0 0 1 r r r a v ae v r. This equation can be simpli ed with two substitutions. In the present study we confirm on the schrodinger equation as a special case for a sturmliouville equation, then the numerov method is used and prepared to check its algorithm for the eigenvalues of the harmonic oscillator potential then it is used to find the eigenvalues for the woodsaxon potential. One solution is obtained analytically by means of the hypergeometric series. The single particle energies and the single particle wave functions are calculated from onebody hamiltonian including a central. The radial equation for the coulomb potential can then be solved along the same lines as for the harmonic oscillator, sect.
Scattering of woodssaxonpotential in schrodinger equation. The timeindependent schroedinger equation a very important special case of the schroedinger equation is the situation when the potential energy term does not depend on time. Saxon the form of the potential, in terms of the distance r from the center of. Study of quantum turbulence with the exponential potentials. Approximate scattering and bound state solutions of the onedimensional effectivemass dirac equation with the woodssaxon potential are obtained in. We could now in principle proceed to rewrite the secondorder di erential equation. A common potential that is used to represent the strong interaction between a nucleon and the rest of the nucleus is the woodssaxon potential. The onedimensional schr odinger equation 9 and the reduced radial equation can both be written in the form 00x fx x. The type of a nuclear potential spherically symmetric. In fact, the general form of the schrodinger equation is known as the timedependent schrodinger equation tdse.
Koksal department of engineering physics, university of gaziantep, 27310, gaziantepturkiye abstract the s. J theor appl phys solutions of ddimensional schrodinger equation for woods saxon potential with spinorbit, coulomb and centrifugal terms through a new hybrid numerical fitting nikiforovuvarov method a. Newtons method and energy eigenvalue problems for the. Akpan 26 solve the radial schrodinger equation for more general woodssaxon potential mgwsp using nikiforovuvarov method. This potential follows a similar form as the experimental nuclear density distribution.
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