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## (non)typos in byron and fuller’s mathematics of classical and quantum physics?

Posted by peeterjoot on March 26, 2009

Dover doesn’t have an errata page for this (excellent) book. I’ve noticed a lot of i’s that look like l’s in the earlier chapters, but am not sure those are typos or just printing quirks. One typo that I was initially pretty sure of was:

page 129 (QM one dimensional harmonic oscillator solved with eigenvalue methods) the Gaussian integral evaluation isn’t right (factor of 2 error).

Suppose one wants

$I = \int_{-\infty}^\infty e^{-\alpha x^2/2} dx$

then the square, after the usual polar coordinates change of variables trick, is

$I^2 = 2 \pi \int_0^\infty e^{-\alpha r^2/2} r dr = \frac{2\pi}{\alpha}$

Doesn’t this then give you a factor of two in along with the $\hbar$ in the expression for $N_0$?

Am I mistaken? Because the book is so old I’d have thought errors like this would be fixed, which makes me doubt myself somewhat.

Ah… I’m dumb! The integral is $\int {\lvert u_0 \rvert}^2$ and that square gets rid of the factor of two in the exponential. Everything is cool in the text, and writing out my bogus argument on why it was wrong resolves the internal dispute without casualties!