Analytic solutions for vibrational energy levels of the pseudoharmonic potential

Abstract

The non-relativistic analytic solutions of a quantum mechanical system have been calculated for the case of pseudoharmonic potential by using the Whittaker functions approach. A diatomic quantum system is placed in a Pseudoharmonic potential and perturbed by an external magnetic field. The resulting Schrodinger’s equation has been solved exactly to obtain the analytic expressions of vibrational energy levels and associated wave functions. In this work, we have compared the results of six diatomic molecules with those available in the literature.

Impact of topological defects and Yukawa potential combined with inverse square on eigenvalue spectra of diatomic molecules O 2, NO, LiH, HCl

“…After a few transformations, the radial equation was expressed as a homogeneous second-order differential equation and solved using the parametric NU-method. The energy levels are presented in equation (14). In the limit α → 1, we presented the energy eigenvalue of non-relativistic particle in the presence of superposed potential in flat space background given in equation (15).…”

“…The exact and approximate eigenvalue solutions of the Schrödinger equation (SE) with these interacting potentials are important in different branches of physics and chemistry. In addition, few exactly solvable potential models well-known in the literature are Coulomb potential (such as in the hydrogen atom problem) and harmonic oscillator problem [9][10][11], pseudoharmonic potential [12][13][14] and Mie potential [15][16][17]. It's worth noting that the non-relativistic wave equation, as described by the Schrödinger equation, has been extensively studied in flat space backgrounds or we called Minkowski space within the context of quantum gravity theory.…”

Time correlation function and average energy of molecules in presence of Deng-Fan potential in a moving boundary

“…This has remained an active area of research covering a large span of time, with widespread applications in molecular spectroscopy atom/molecule adsorption on solid surface, deformation of cubic metal, etc. Some important and popular models for vibrational interactions in molecules are as follows: Manning-Rosen [2][3][4][5], Húlthen [6][7][8][9], Woods-Saxon [10,11], Pöschl-Teller [5,12,13], Tietz-Hua [14][15][16], pseudoharmonic [17][18][19], Rosen-Morse [20][21][22], Kratzer [23,24], Eckart [25] and so on.…”

Time-correlation function and average energy of molecules in presence of Deng-Fan potential in a moving boundary

“…This has remained an active area of research covering a large span of time, with widespread applications in molecular spectroscopy atom/molecule adsorption on solid surface, deformation of cubic metal, etc. Some important and popular models for vibrational interactions in molecules are as follows: Manning-Rosen [2][3][4][5], Húlthen [6][7][8][9], Woods-Saxon [10,11], Pöschl-Teller [5,12,13], Tietz-Hua [14][15][16], pseudoharmonic [17][18][19], Rosen-Morse [20][21][22], Kratzer [23,24], Eckart [25] and so on.…”