# Mistake in Ballentine's book?

1. Jan 3, 2010

### Derivator

Hi folks,

I'm just reading Ballentine's book on quantum mechanics and was wondering whether he really made a mistake. It's about the variational principle.

In chapter 10.6 (p. 296 in the current edition) he says:

Shouldn't

$$<\psi|\mathcal{H}|\psi> {\color{red}\geq} E_m \sum_n |<\psi|\Psi_n>|^2 = E_m <\psi|\psi>$$

?

--derivator

Last edited: Jan 3, 2010
2. Jan 3, 2010

### strangerep

I sure hope it's a typo. (Otherwise I don't understand it either. :-)

I think it should indeed be $$\geq$$ , since otherwise it doesn't make sense
to "minimize" the ratio to get the eigenvalue. The $$\geq$$ is also what he
wrote in the previous Variational theorem on pp291-292.

Googling for "ballentine quantum errata" produced a few hits, but nothing
comprehensive, afaict. I sure wish Prof Ballentine and/or the publishers
would compile an errata list. One of the later chapters seemed to have
an elevated number or errors, as I recall. Maybe it didn't get good proofreading.