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Mistake in Ballentine's book?

  1. Jan 3, 2010 #1
    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:



    [tex]<\psi|\mathcal{H}|\psi> {\color{red}\geq} E_m \sum_n |<\psi|\Psi_n>|^2 = E_m <\psi|\psi>[/tex]


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


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    Science Advisor

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

    I think it should indeed be [tex]\geq[/tex] , since otherwise it doesn't make sense
    to "minimize" the ratio to get the eigenvalue. The [tex]\geq[/tex] 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.
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