[問題]量力習題解惑

[iandddy0986 (BOOK)]

【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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→ kerwinhui: H = sum_{m,n} |m> <m|H|n> <n|
→ kerwinhui: 所以…
→ iandddy0986: 謝謝ker大的提示!