1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof for Problem 1.1.1 of Shankars Prin of QM

  1. Jul 2, 2011 #1
    I think I may be over-thinking this as I have had one formal course in QM and an independent study course in QM, but any help is MORE THAN GREATLY APPRECIATED!!!

    1. The problem statement, all variables and given/known data

    Prove that |-V> = -|V>

    2. Relevant equations

    He instructs us to begin with |V> + (-|V>) = 0|V> = |0>

    3. The attempt at a solution

    Let -|V> = |W>


    |V> + |W> = 0|V> = |0>

    which implies that

    |W> = |-V> ?

    I'm really confused.
  2. jcsd
  3. Jul 4, 2011 #2
    Okay, first I think you mean problem 1.1.2, unless you have a different edition.
    This is the kind of proof where you have to doubt everything. Act as if you are in a mathematical minefield. Only do the things you can completely justify.

    I find myself wanting to say that 1V = V, but that actually isn't an axiom...

    Assuming that for the moment,
    V + (-1)V = 1V + (-1)V = (1 + -1)V = 0V = 0 (by part 1 of the same problem)
    And thus (-1)V is the unique vector -V such that V + -V = 0

    Looking up in other books, 1V = V is listed as an eighth axiom for linear spaces. Shankar described it by interpretation in a paragraph, but didn't actually state it overtly as an axiom.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Proof for Problem 1.1.1 of Shankars Prin of QM
  1. QM - Shankar 12.6.1 (Replies: 4)

  2. Shankar problem 14.4.3 (Replies: 1)