Calculation of displacement matrix elements for Morse oscillators

Displacement matrix elements of the Morse oscillators are widely used in physical and chemical computation. Many papers have been published about the analytical expressions of the displacement matrix elements. People still use an integration method rather than the analytical expressions to calculate the displacement matrix elements. Analytical expressions of the diagonal and off diagonal displacement matrix elements <nu+m\q(n)\m> with intermediate variables are derived, where nu, m and n are non-negative integers and n . 6. Calculation with these expressions is superior to that with numerical integration in precision, calculation speed and convenience.