ps3q3 - Question: On page 39 of the professor's notes, he...

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Question: On page 39 of the professor’s notes, he said the elements of U were h i 0 | j i instead of h i | j 0 i . Anyone who followed that example would have done Problem 3 of homework 3 wrong. When Prof. Nelson talks about transforming matrix elements on page 40, he gets the boxed equation, Ω il = X jk U ij Ω 0 jk U kl which transforms the matrix elements of the “primed” representation of Ω into the matrix elements in the unprimed representation. From the line above that, U kl = h k 0 | l i and U ij = h i | j 0 i is its adjoint. The way I’ve been deriving these things in my solutions is by inserting a decomposition of unity. If I do that for the components of a vector, v 0 j 0 = h j 0 | v i = X i h j 0 | i ih i | v i = X i h j 0 | i i v i Comparing with the previous paragraph, I can identify the braket h j 0 | i i = U ji and write h j | v i = X i U ji h i | v i This is the same thing that Prof. Nelson has on page 39–there’s no mistake. I think the confusing thing is that in Prof. Nelson’s notes,
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ps3q3 - Question: On page 39 of the professor's notes, he...

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