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本文将单点杂质引入到不可共度势一维体系中,用格林函数方法推导了杂质状态的能级和波函数。发现当杂质处在不可共度势变化较快的位置时,杂质能级的变化也较大。杂质状态的波函数是略有波动的指数衰减函数。讨论了杂质对带内状态波函数的影响,发现以杂质点为对称的体系中,具有偶宇称的状态波函数,在杂质的附近,振幅有相当大的下降。在对杂质点无对称性的体系中,在杂质的附近,产生一个振幅的阶跃。We study the effect of a single impurity in a one dimensional system with incommensurate lattice potential. The energy level and the wavefunction of the impurity State is derived with the Green's function technique. The energy level is found to be very sensitive to the impurity position in the region where the incommensurate potential is varying rapidly. The wavefunction of the impurity state decays exponentially with small oscillation of the amplitude. We also consider the effect of the impurity on the states in the band. For a system that is symmetric about the impurity, we find a large reduction of the amplitude of the wavefunction with even parity in the vicinity. For a system that is asymmetric about the impurity, a step-wise increase in the amplitude occurs at the impurity.
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