Schrodinger equation Morse oscillator

The authors in this paper present an explicit symplectic method for the numerical solution of the Schrodinger equation. A modified symplectic integrator with the trigonometrically fitted property which is based on this method is also produced. Our new methods are tested on the computation of the eigenvalues of the one-dimensional harmonic oscillator, the doubly anharmonic oscillator and the Morse potential. 

Note that V (Rg) = 0 at the minimum of the potential well. The Schrodinger equation for a Morse oscillator can be solved to give the energy levels... 

In 34 the eigenvalue problem of the one-dimensional time-independent Schrodinger equation is studied. Exponentially fitted and trigonometrically fitted symplectic integrators are developed, by modification of the first and second order Yoshida symplectic methods. Numerical results are presented for the one-dimensional harmonic oscillator and Morse potential. 

An exact solution of the Morse oscillator Schrodinger equation yields... 

Here r, r, and are the atomic distance, equilibrium bond length, and potential-well depth, respectively. Further, h is Planck s constant and c is the light velocity in vacuum. The potential-curve shapes depend on the parameters and D. By analytically solving the Schrodinger equation with the anharmonic potential (Equation 2.3), one can obtain the vibrational energy levels ofthe Morse molecular oscillator ... 

Spatially-Dependent-Mass Schrodinger Equations with Morse Oscillator Eigenvalues Isospectral Potentials and Factorization Operators... 

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