Novel bound states treatment of the two dimensional Schrödinger equation with pseudocentral potentials plus multiparameter noncentral potential (original) (raw)
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Il Nuovo Cimento B, 1999
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International Research Journal of Pure and Applied Physics, 2019
In this paper, we studied the approximate bound-state solutions of the radial Schrodinger equation with a quantum mechanical Gaussian potential, by using the generalized parametric Nikiforov-Uvarov method. The energy spectrum and the corresponding wave function were obtained analytically in closed form. The computed eigenvalues for the ground state and first excited state for sufficiently large potential depths are in good agreement with the results obtained with other methods.
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Computer Physics Communications, 1985
Title ofprogram; SCR2 ments, scale transformation, numerical integration, convexity arguments, node theorem Catalogue number; ACDQ Nature of the physical problem Program obtainable from; CPC Program Library, Queen's Uni-SCR2 calculates energy levels and wave functions of the rotaversity of Belfast, N. Ireland (see application form in this issue) tional symmetric Schrodinger equation for a given potential using a simple and accurate method. Computer. VAX 11/750; Installation; Prozessrechenanlage Physik, Universität Wien Method ofsolution An iterative procedure for getting upper and lower bounds to Operating system; VMS 35 energy values of the radial Schrodinger equation is given. A numerical integration procedure together with convexity argu-Note; SCR2 runs also on the CDC CYBER 170/720 without ments and the nodal theorem for wave functions is used. modifications Typical running time Programming language u.sed. USANSI FORTRAN 77 5 s for one bound state. Note; The running time depends strongly on the desired accuracy. Program size; 2 Kbyte References No. of bits in a word; 32 [1) For applications see: H. Grosse and A. Martin, Phys. Rep. 60 (1980) 341. No. oflines in combinedprogram and test deck; 274 [2] M. Abramowitz and l.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968).
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.