Novel bound states treatment of the two dimensional Schrödinger equation with pseudocentral potentials plus multiparameter noncentral potential (original) (raw)
Bound state solutions of the two--dimensional Schr\"{o}dinger equation with Kratzer--type potentials
arXiv (Cornell University), 2023
Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schrödinger equation is applied for a solution of a two-dimensional (2D) problem for two particles interacting via Kratzer, and modified Kratzer potentials. We found the exact bound state solutions of the two-dimensional Schrödinger equation with Kratzer-type potentials and present analytical expressions for the eigenvalues and eigenfunctions. The eigenfunctions are given in terms of the associated Laguerre polynomials.
The generalized pseudospectral approach to the bound states of Hulthen and Yukawa potentials
2013
The generalized pseudospectral method is employed to calculate the bound states of Hulth\'en and Yukawa potentials in quantum mechanics, with special emphases on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a nonuniform and optimal spatial discretization of the radial Schr\"odinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials with nleqn\leqnleq10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high as up to n=17n=17n=17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. The n>6n>6n>6 states of Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulth\'en potential are reported here for the first time. Excepting the 1s1s1s and 2s2s2s states of Yukawa potential, the present method surpasses in accuracy all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials.
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.
Eprint Arxiv Quant Ph 0703131, 2007
We present analytically the exact energy bound-states solutions of the Schrödinger equation in D-dimensions for a pseudoharmonic potential plus ring-shaped potential of the form V (r, θ) = D e r re − re r 2 + β cos 2 θ r 2 sin 2 θ by means of the conventional Nikiforov-Uvarov method. We also 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 pseudoharmonic 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 the literature.
Exact solutions of the radial Schrödinger equation for some physical potentials
Open Physics, 2007
By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.
Approximate Bound State Solutions for Certain Molecular Potentials
Journal of Applied Mathematics and Physics, 2021
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.
Bound state solutions to the Schrödinger equation for some diatomic molecules
Pramana, 2018
The bound state solutions to the radial Schrödinger equation are obtained in three-dimensional space using the series expansion method within the framework of a general interaction potential. The energy eigenvalues of the pseudoharmonic and Kratzer potentials are given as special cases. The obtained analytical results are applied to several diatomic molecules, i.e. N 2 , CO, NO and CH. In order to check the accuracy of the present method, a comparison is made with similar results obtained in the literature by using other techniques.
Pramana-journal of Physics, 2009
We deal with the difficulties claimed by the author of [Ann. Phys. 206, 90 (1991)] while solving the Schrödinger equation for the ground states of two-dimensional anharmonic potentials. It is shown that the ground state energy eigenvalues and eigenfunctions for the coupled quadratic and quartic potentials can be obtained by making some simple assumptions. Expressions for the energy eigenvalues and the eigenfunctions for the first and second excited states of these systems are also obtained.
The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials
Pramana, 2005
The generalized pseudospectral (GPS) method is employed to calculate the bound states of the Hulthén and the Yukawa potentials in quantum mechanics, with special emphasis on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a non-uniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials with n ≤ 10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high as n = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. The n > 6 states of the Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of the Yukawa potential, the present method surpasses the accuracy of all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials.
2021
A theoretical analytical investigation for the exact solvability of non-relativistic quantum spectrum systems, at low energy for modified two-dimensional purely sextic double-well potential (2D-modified sextic DWAO potential) is discussed, by means Bopp's shift method, instead to solving deformed Schrödinger equation with star product, in the framework of both noncommutativite two dimensional real space and phase (NC: 2D-RSP), the exact corrections for lowest excitations are found straightforwardly for interactions in one-electron atoms by means of the standard perturbation theory for three special cases. Furthermore, the obtained corrections of energies are depended on the four infinitesimals parameters ( , ) and ( , ), which are induced by position-position and momentum-momentum noncommutativity, respectively, in addition to the discreet atomic quantum numbers ( ) and the magnetic quantum number m . We have also generalized our obtained results to include the other atoms with spin 2 / 1 S .