This paper deals with the interesting topic of the interaction of polarons with lattice vibration with the emergence of soliton solutions in one-dimensional molecular crystals,the nonlinear Schrodinger eguation for the polaron probability amplitude follows by the use of vibration configuration resulting from the energy minimum.

The two-slit and multiple-slit diffraction of electrons have been analyzed by probability amplitude of momentum representation in quantum theory,and the results are in keeping with light s.

Starting with the transition probability amplitudes of the radiation-molecule interactions,the correspondence is shown between the energy level diagrams and the time-ordered graphs for several two-photon processes and the perturbational matrix elements of the interactions.

By using the transition probability amplitudes of the Rayleigh and Raman scattering,quantum mechanical expression for the prolarizability of a molecule subjected to electromagnetic wave is introduced.

The momentum probability amplitude and the equality form uncertainty relation of one dimensional infinite well;

In this paper,the uncertainty in positon,the momentum probability amplitude and momentum probability density s recurrence formulas,the uncertainty in momentum and the uncertain relation of the equality form momentum-position of one-dimensional harmonic oscillator were deduced.