作者nightkid (约束された胜利の剣)
看板Physics
标题[问题] 基底向量与本徵值
时间Sat Apr 18 14:24:32 2009
as title
如果我一个Hamiltonian : H 使用某一基底向量展开 可得一组本徵值
若是使用么正矩阵将其对角化 (U+)H(U) (意即将H的基底向量换为其本徵向量)
那H的本徵值会改变吗?
我如果使用不同的矩阵: <ri| H |r'j> 可得到另一矩阵(表其用另一组基底向量展开)
则这个Hamiltonian的本徵值会改变吗?
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※ 编辑: nightkid 来自: 140.115.218.227 (04/18 14:27)
1F：推 motoman:不会 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:感谢您 thank a lot! 04/18 23:22