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In your solution to Shankar’s Quantum Mechanics, problem 12.03.01, equation 9 and the subsequent ones, you’re missing a factor of rho in the integrand. (The rho is also written in the question, I think it’s a typo)

Also, I think the paragraph after equation 11 does not necessarily prove equation 12.

Thanks for your detailed solutions!

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Fixed now. Thanks.

As for equation 12, in the textbook it says to show that “it is enough if obeys” Shankar’s equation 12.3.6 (my equation 12), which is certainly true, since then the value of in equation 11 is zero.

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