Application Of The Finite-Difference Time-Domain Method In The Quantum Calculation Of The Diatomics Spectrum

Finite-difference time-domain method is a numerical calculation method of finding the solution to the electromagnetic field in the time-domain. It transfers Maxwell Differential Equation with time variant to difference equation so as to find the solution to the electromagnetic field. Since the foundation of FDTD method, it is mainly used in the calculation of the electromagnetic fields and waves. However, there are few reports of the application in the calculation of quantum mechanics.Firstly, the theories and development of the FDTD method were briefly introduced and the traditi6nal method of quantum calculation was offered. The potential energy functions and the spectrums' characteristic of diatomics were analyzed. The application of FDTD method in vibrational spectrums for diatomics was expatiated, and the vibrational spectrums of ground and excited states for oxygen molecule were calculated with this method by the approximate boundary cut-off .Secondly, considering rationality of physical model and the strictness of mathematical logic, a novel method to cut-off the boundary was suggested based on the conversation of energy, which makes FDTD more reasonable in the application for the quantum calculation of diatomics spectrums. The improved boundary cut-off method is applied in the calculation of the vibrational spectrums for the ground and excited states of oxygen.Finally, the spectrum constants were compared with the experimental data and the results are acceptable. Thus it is indicated that FDTD method and the novel boundary cut-off is feasible on the calculating for the vibrational spectrums of diatomics.FDTD method doesn't need a complete basic set of functions to construct the wave function, therefore the contradiction between the infinity of the number of basic functions and the finity of practical calculation is avoided. FDTD method is feasible for the direct time-domain calculation, the development ofcommon program and parallel calculation. The method is simple, convenient and easy to be master, and is a new choice for the quantum calculation.