Where do I mistake please? My computation differ from the result in the text about red terms. Thank you
2026-03-26 02:26:40.1774492000
Substitution - mistake
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When you do the substitution, you do it so that the integral is easier to calculate. $$\int_X|\Psi_0(x)|^2dx=<0|0>=\int_Y|\Psi_0(y)|^2dy$$ That means that you need to account for $\frac{dx}{dy}$ term, or in fact the square root of that.