  Explicit algebraic expressions for the expansion of the vibrational matrix
elements in series of matrix elements on the wave functions of the ground
vibrational state have been obtained for arbitrary sufficiently differentiable
functions of the internuclear distance, arbitrary values v and v', and the
potential curves whose ladder operators can be constructed. A diagram technique
have been developed for it that consists in: 1) the numeration of the matrix
elements by points of the 2D diagram with coordinates (l, k), 2) the drawing
arrows between points of this diagram corresponding to the action of the
annihilation operators on the wave functions; 3) total taking into account of
all possible path vectors formed by the continuous sequences of arrows from
point (v, v) towards points (0, k). The only requirement is that the action of
the operator on the wave functions should give the wave functions of the
Schr\"odinger equation with the potential curve having the same parameter
values. All necessary data for algebraic calculations of the vibrational
dependence of matrix elements for the harmonic oscillator and the Morse
potential have been given. Obtained expressions can be used to determine the
absolute values and vibrational dependences of various spectroscopic
characteristics of both ground and electronically excited states of diatomic
molecules.
