作者nightkid (約束された勝利の剣)
看板Physics
標題[問題] 基底向量與本徵值
時間Sat Apr 18 14:24:32 2009
as title
如果我一個Hamiltonian : H 使用某一基底向量展開 可得一組本徵值
若是使用么正矩陣將其對角化 (U+)H(U) (意即將H的基底向量換為其本徵向量)
那H的本徵值會改變嗎?
我如果使用不同的矩陣: <ri| H |r'j> 可得到另一矩陣(表其用另一組基底向量展開)
則這個Hamiltonian的本徵值會改變嗎?
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◆ From: 140.115.218.227
※ 編輯: nightkid 來自: 140.115.218.227 (04/18 14:27)
1F：推 motoman:不會 04/18 16:21
2F：→ covari:no. 04/18 16:22
3F：推 copyxee:From some points of view, when you measure a quantity 04/18 16:58
4F：→ copyxee:"A" what you will get is nothing but the expectation 04/18 16:59
5F：→ copyxee:of quantity "A", and we know that the expectation of 04/18 17:00
6F：→ copyxee:"A" is just some linear combination of its eigenvalues 04/18 17:00
7F：→ copyxee:so the eigenvalues of "A" are invariant under basis 04/18 17:02
8F：→ copyxee:transformation. 04/18 17:02
9F：推 copyxee:Sorry,I should pinpoint that expectation values of "A" 04/18 17:06
10F：→ copyxee:are independent of representation of "A". 04/18 17:07
11F：→ nightkid:感謝您 thank a lot! 04/18 23:22