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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? -- Our destiny have been entwined,Jenny, but never joined... -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.115.218.227 ※ 編輯: nightkid 來自: 140.115.218.227 (04/18 14:27)
motoman:不會 04/18 16:21
covari:no. 04/18 16:22
copyxee:From some points of view, when you measure a quantity 04/18 16:58
copyxee:"A" what you will get is nothing but the expectation 04/18 16:59
copyxee:of quantity "A", and we know that the expectation of 04/18 17:00
copyxee:"A" is just some linear combination of its eigenvalues 04/18 17:00
copyxee:so the eigenvalues of "A" are invariant under basis 04/18 17:02
copyxee:transformation. 04/18 17:02
copyxee:Sorry,I should pinpoint that expectation values of "A" 04/18 17:06
copyxee:are independent of representation of "A". 04/18 17:07
nightkid:感謝您 thank a lot! 04/18 23:22