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本文采用的方法是,在一维方势籍中,引人周期为单键与双键长度之和的余弦型势函数。将适合附加条件的薛定谔方程经过变换,化成适合边界条件的马蒂安方程,利用逐步求解法,得出包含一个参数 q 的能量及波函数的级数表达式。经过一些计算,便推导出第一吸收峰的波数公式(9)和振子强度的理论公式(11)。应用这两个公式解释多烯烃及双苯基多烯烃的光谱时,结果还比较满意,利用这种近似,也解释了不对称的聚甲川分子的实验数据。当 q=0,α=0,时,非常自然地推导出简单自由电子理论公式,满意地解释了对称聚甲川分子的实验数据。根据自由电子模型,对维特经典色泽理论的结果,也在文中示例予以阐明。
The method used in this paper is to introduce the cosine type potential function whose sum is the sum of the length of the single bond and the double bond in one dimension. The Schrödinger equation which is suitable for the additional conditions is transformed into the Martian equation which is suitable for the boundary conditions. By using the stepwise solution method, the expression of the series of energy and wave functions with a parameter q is obtained. After some calculation, the wave number formula (9) of the first absorption peak and the theoretical formula (11) of the oscillator strength are deduced. Using these two formulas to explain the spectra of polyolefins and diphenyl polyolefins, the results are still quite satisfactory. Using this approximation, we also explain the experimental data of asymmetric polymethine molecules. When q = 0 and α = 0, simple free-electron theoretical formulas are derived very naturally and the experimental data of symmetric polymethrin molecules are satisfactorily explained. According to the free electron model, the result of Wittmann’s classical color theory is also illustrated in the text.