[問題] 量力習題解惑
【出處】量子力學習題
【題目】
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.
【瓶頸】
題目要我把 H operator用Dirac notation表示.
他有提到要把系統discretized,但我不知道怎麼起頭,
也試著把 H operator ; f_n ; state ∣n＞ 連結在一起,不過都沒成功.
請各位版友可以給我提示讓我知道可以從何下手,感謝!!
小弟初學量力,請多包涵.
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