Exact solutions for vibrational levels of the Morse potential
نویسنده
چکیده
The vibrational levels of diatomic molecules via Morse potentials are studied by means of the system confined in a spherical box of radius `. It is shown that there exists a critical radius `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 (−∞, 0). By determining numerically exact lower and upper bounds for the energy eigenvalues of Li2 molecule, it is deduced here that Morse’s approach is perfect and gives very impressive results.
منابع مشابه
Approximate Ro-Vibrational Spectrum of the Modified Rosen–Morse Molecular Potential Using the Nikiforov–Uvarov Method
In many fields of physics and chemistry, explicit analytical solutions of the fundamental dynamical equations are much valuable for a general understanding of phenomena, e. g. the role played by physical parameters. Two typical examples in quantum mechanics are the exact solutions of the Schrödinger equation (SE) for a hydrogen atom (Coulombic) and for a harmonic oscillator [1 – 3]. The Mie-typ...
متن کاملInvestigation of analytical and numerical solutions for one-dimensional independent-oftime Schrödinger Equation
In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...
متن کاملOn the variational solution of morphed molecular potential in a diatomic molecule
The general one-dimensional potential energy function, including centrifugal distortion, for a diatomic molecule is morphed with a series of Morse-like functions for each of the rotational quantum numbers J . For each of the morphed potential, explicit formulae for the matrix elements of the complete energy matrix, on the basis of the solutions of the one-dimensional harmonic oscillator, are gi...
متن کاملSystematic calculation of molecular vibrational spectra through a complete Morse expansion
We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard LennardJones oscillator, and to the ab-initio potential of the H2 molecule. ...
متن کاملExact solutions of distinct physical structures to the fractional potential Kadomtsev-Petviashvili equation
In this paper, Exp-function and (G′/G)expansion methods are presented to derive traveling wave solutions for a class of nonlinear space-time fractional differential equations. As a results, some new exact traveling wave solutions are obtained.
متن کامل