Exact solutions for vibrational levels of the Morse potential

The vibrational levels of diatomic molecules via Morse potentials are studied by means of the system confined in a spherical box of radius l, II is shown that there exists a critical radius l(cr),, at which the spectrum of the usual unbounded system can be calculated to any desired accuracy. The results are compared with those of Morse's classical solution which is based on the assumption that the domain of the internuclear distance r includes the unphysical region (-infinity, 0). By determining numerically exact lower and upper bounds for the energy eigenvalues of Li-2 molecule, it is deduced here that Morse's approach is perfect and gives very impressive results.


Pseudospin symmetry solution of the Dirac equation with an angle-dependent potential
Berkdemir, Cueneyt; Sever, Ramazan (IOP Publishing, 2008-02-01)
The pseudospin symmetry solution of the Dirac equation for spin 1/2 particles moving within the Kratzer potential connected with an angle-dependent potential is investigated systematically. The Nikiforov-Uvarov method is used to solve the Dirac equation. All of the studies are performed for the exact pseudospin symmetry (SU2) case and also the exact spin symmetry case is given briefly in the appendix. Bound-state solutions are presented to discuss the contribution of the angle-dependent potential to the rel...
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We investigate the minimum energy configuration of N equal point charges interacting via the Coulomb potential 1/r, and placed on an infinitely thin conducting disk. By minimizing total interaction Energy, we obtain numerically the minimum energy configurations from which the rules for the distribution of charges on the disk are obtained.
String-Theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
Kondo, Satoshi; Watari, Taizan (Springer Science and Business Media LLC, 2019-04-01)
It is known that the L-function of an elliptic curve defined over Q is given by the Mellin transform of a modular form of weight 2. Does that modular form have anything to do with string theory? In this article, we address a question along this line for elliptic curves that have complex multiplication defined over number fields. So long as we use diagonal rational N=(2,2) superconformal field theories for the string-theory realizations of the elliptic curves, the weight-2 modular form turns out to be the Bo...
Singular potentials and moving boundaries in 3D
Yuce, C (Elsevier BV, 2004-02-16)
In this Letter, the problem of a spinless particle under the time-dependent harmonic oscillator potential and a singular potential with a moving boundary is studied in the spherical coordinates. Some transformations are used to transform the moving boundary conditions to the fixed boundary conditions. An exact solution is constructed.
Akturk, Ethem; ÖZCAN, ÖZGÜR; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2009-04-30)
Time-dependent joint entropy is obtained for harmonic oscillator with the time-dependent mass and frequency case. It is calculated by using time-dependent wave function obtained via Feynman path integral method. Variation of time dependence is investigated for various cases.
Citation Formats
H. Taşeli, “Exact solutions for vibrational levels of the Morse potential,” JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, pp. 779–788, 1998, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48375.