Exact quantization rule to the Kratzer-type potentials: an application to the diatomic molecules

Abstract

For any arbitrary values of n and l quantum numbers, we present a simple ex-

An alternative solution of diatomic molecules

“…which is exactly the same as the eigenvalue equation obtained in [51,52] through a proper choice of parameters.…”

“…(19). A new type of this potential is called the modified Kratzer potential and it is given by [51][52][53][54] …”

Bound States of the Klein-Gordon for Exponential-Type Potentials in D-Dimensions

“…Quite recently, we have also proposed a new approximation scheme for the centrifugal term [13,14]. The Nikiforov-Uvarov (NU) method [60] and other methods have also been used to solve the D-dimensional Schrödinger equation [61] and relativistic D-dimensional KG equation [62], Dirac equation [6,15,39,40,63] and spinless Salpeter equation [64].…”

Exact quantization formula for affine linearly energy-dependent potentials

“…As was shown recently [12], in case more information about the quantum system is available, then the Bohr-Sommerfeld rule can be modified to deliver exact results: knowledge of the potential and the quantum system's ground state are sufficient to predict the entire discrete energy spectrum in closed form. The such modified Bohr-Sommerfeld rule (called exact quantization formula) has been successfully tested on potentials that admit a discrete spectrum, including the Coulomb and harmonic oscillator case [12], Kratzer-type potentials [10], hyperbolic and Pöschl-Teller-like potentials [4], modified RosenMorse potentials [9], and many more. In contrast to these numerous applications in the conventional Schrödinger case, very little is known about quantization formulas and their application to other quantum-mechanical equations, such as the position-dependent mass Schrödinger equa-tion [16].…”