KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 33Σg+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 33Σg+ state of Cs2 and the 51Δg state of Na2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.

Download Full-text

Doubly excited states ofH−and He in the coupled-channel hyperspherical adiabatic approach

Physical Review A ◽

10.1103/physreva.45.5274 ◽

1992 ◽

Vol 45 (7) ◽

pp. 5274-5277 ◽

Cited By ~ 15

Author(s):

A. G. Abrashkevich ◽

D. G. Abrashkevich ◽

M. S. Kaschiev ◽

I. V. Puzynin ◽

S. I. Vinitsky

Keyword(s):

Excited States ◽

Doubly Excited States ◽

Adiabatic Approach ◽

Doubly Excited ◽

Hyperspherical Adiabatic ◽

Coupled Channel

Download Full-text

Theoretical studies in nuclear structure III. Radial integrals for the nuclear s, p and d shells

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1951.0027 ◽

1951 ◽

Vol 205 (1081) ◽

pp. 238-246 ◽

Cited By ~ 24

Keyword(s):

Nuclear Structure ◽

Interaction Potential ◽

Nuclear Energy ◽

Energy Levels ◽

Three Dimensional ◽

Wave Functions ◽

Theoretical Studies ◽

Hartree Approximation ◽

Radial Wave ◽

Working Out

In working out nuclear energy levels on the Hartree approximation one meets certain integrals involving the interaction potential and the particle radial wave-functions (see parts I and II by H. A. Jahn (1950, 1951) in the present series). In this note these integrals are defined and worked out for the 1 s , 2 p , 3 d wave-functions of a three-dimensional oscillator using as interaction potential ( a ) the Gauss potential, ( b ) the meson potential.

Download Full-text

The bound state solutions of the D-dimensional Schrödinger equation for the Hulthén potential within SUSY quantum mechanics

International Journal of Modern Physics E ◽

10.1142/s0218301317500288 ◽

2017 ◽

Vol 26 (05) ◽

pp. 1750028 ◽

Cited By ~ 7

Author(s):

H. I. Ahmadov ◽

M. V. Qocayeva ◽

N. Sh. Huseynova

Keyword(s):

Quantum Mechanics ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Dimensional Space ◽

Energy Levels ◽

Wave Functions ◽

Hulthén Potential ◽

Radial Wave ◽

Energy Eigenvalues ◽

Hulthen Potential

In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.

Download Full-text

METODE ELEMEN HINGGA UNTUK PENYELESAIAN PERSAMAAN SCHRÖDINGER ATOM HIDROGENIK

Jurnal Matematika Sains dan Teknologi ◽

10.33830/jmst.v7i1.623.2006 ◽

2006 ◽

Vol 7 (1) ◽

pp. 11-23

Author(s):

Paken Pandiangan ◽

Supriyadi Supriyadi ◽

A Arkundato

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Hydrogen Atom ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Energy Levels ◽

Wave Functions ◽

Radial Wave ◽

Action Integral ◽

Method Approach

The research computed the energy levels and radial wave functions of the Hydrogen Atom. The method used for computation was FEM (finite element method). Using the variational method approach, FEM was applied to the action integral of Schrödinger equation. This lead to the eigenvalue equation in the form of global matrix equation. The results of computation were depended on boundary of the action integral of Schrödinger equation and number of elements. For boundary 0 - 100a0 and 100 elements, they were the realistic and best choice of computation to the closed analytic results. The computation of first five energy levels resulted E1 = -0.99917211 R∞, E2 = -0.24984445 R∞, E3 = -0.11105532 R∞, E4 = -0.06247405 R∞ and E5 = -0.03998598 R∞ where 1 R∞ = 13.6 eV. They had relative error under 0.1% to the analytic results.

Download Full-text

Analytical solution of the Duffin - Kemmer - Petiau equation for the sum of the Manning - Rosen and the Yukawa class potential

Izvestiya vysshikh uchebnykh zavedenii. Fizika ◽

10.17223/00213411/64/7/140 ◽

2021 ◽

pp. 140-150

Author(s):

S.M. Aslanova ◽

Keyword(s):

Hypergeometric Functions ◽

Energy Levels ◽

Energy Eigenvalue ◽

Bound State ◽

Wave Functions ◽

State Solution ◽

Bound State Solution ◽

Radial Wave ◽

Quantum Numbers ◽

Analytical Expressions

This paper presents an analytical bound-state solution to the Duffin - Kemmer - Petiau equation for the new putative combined Manning - Rosen and Yukawa class potentials. Using the developed scheme to approximate and overcome the difficulties arising in the centrifugal part of the potential, the bound-state solution of the modified Duffin - Kemmer - Petiau equation is found. Analytical expressions of energy eigenvalue and the corresponding radial wave functions are obtained for an arbitrary value of the orbital quantum number l . Also, eigenfunctions are expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are quite sensitive to the choice of radial and orbital quantum numbers.

Download Full-text