推 pleasetoyou:很像有筆誤喔 04/10 19:24
→ pleasetoyou:其實我也不確定,正在驗算第三題 04/10 19:25
推 phy888:;D 應該是對的 04/10 22:54
psi 太麻煩懶得按 用z代替, exp裡面的東西懶得打 用exp(...)代替 反正你知道就好
hbar = h , omega = w
dz/dx = -ax exp(...) f(x) + exp(...) f'(x)
d^2 z/dx^2 = d(z')/dx = -a exp(...) f(x) + (ax)^2 exp(...) f(x)
-ax exp(...) f'(x) -ax exp(...) f'(x) + exp(...) f"(x)
= (-a + (ax)^2) exp(...) f(x) + -2ax exp(...) f'(x) + exp(...) f"(x)
代回去Schroedinger eq.
-h^2/2m z" + 0.5kx^2 z = Ez
大家都有exp(...) 消去
-h^2/2m [(-a+(ax)^2)f - 2axf' + f")] + 0.5kx^2 f - Ef =0
a = mw/h 代入 , k = mw^2 (harmonic oscillator)
0.5hw f + 0.5mw^2 x^2 f - 2mwx/h f' + h^2/2m f" + 0.5kx^2 f - Ef =0
h^2 /2m f" - 2mw/h x f' - (E - 0.5hw)f = 0
f" - 2 (...)x f' - (...)*(E - 0.5hw) f = 0
令 (...)x = X , 2*(...)*(E - 0.5hw) = 2n
f" - 2X f' - 2n f = 0 => Hermite eq.
這樣有錯嗎?
※ 引述《phy888 (神隱少女)》之銘言：
: 這是考古題
: 我有試著把 PSI 微分 可是還是不會導
: 導不出 hermite equation
: 題目如圖:http://ppt.cc/EVDR
: 如果大大會 請教我~~~~感恩
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I have finished over a thousand assignments.
Unknown to pass. Nor known to fail.
Have withstood pain to take many midterms.
Yet, those hands will never write anything.
So as I pray, Unlimited homeworks.
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※ 編輯: nightkid 來自: 140.115.220.100 (04/10 18:31)