【出处】量子力学习题 【题目】 Consider a particle governed by H = (-h^2/2m)d^2/dx^2+V(x). Now, if the particle is further confined to be at x = na with n be integers and a being a positive constant,one needs to discretize the system: replacing any function f(x = na) by fn and d^2/dx^2Ψ(x)∣x=na by [ (Ψn+1) + (Ψn-1) +2Ψn)] /a^2 . Let us denote the state when the particle is localized at x = na by ∣n＞ and assume that ＜n∣m＞=δnm. Express H in terms of the Dirac notations. 【瓶颈】 题目要我把 H operator用Dirac notation表示. 他有提到要把系统discretized,但我不知道怎麽起头, 也试着把 H operator ; f_n ; state ∣n＞ 连结在一起,不过都没成功. 请各位版友可以给我提示让我知道可以从何下手,感谢!! 小弟初学量力,请多包涵. --

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