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!

Changing bases (with bra-ket notation)

  1. Jan 18, 2014 #1

    i don't understand why the old base is written in terms/as a linear combination of the new bases. wouldn't i want to map my coordinates from old to new not new to old?..

    here's what my textbook says about it, can you guys interpret this for me, i still don't get it..

    (it's the stuff of the red outline)

  2. jcsd
  3. Jan 18, 2014 #2


    User Avatar
    Science Advisor
    Gold Member

    Let's say you have an arbitrary vector written in terms of the old basis. Is it easier to write it in terms of the new basis knowing what each of old basis vectors are in the new basis, or is it easier to start by knowing what the new basis vectors are in the old basis?
  4. Jan 18, 2014 #3
    i don't follow; how are the two any different?

    in both cases it sounds like i'm writing the new basis in terms of the old. can you elaborate on what you mean?
  5. Jan 19, 2014 #4


    User Avatar
    Science Advisor
    Gold Member

    Given a vector:

    [tex]|v\rangle = \sum^n_{j=1} x_j|e_j\rangle[/tex]

    and that

    [tex]|e_j\rangle = \sum^n_{i=1} S_{ij}|f_i\rangle[/tex]


    [tex]|v\rangle = \sum^n_{j=1}\sum^n_{i=1}x_j S_{ij}|f_i\rangle[/tex]

    Or in other words knowing how to express the old basis vectors in terms of the new basis vectors tells you how to express a vector in the new basis given it's expression in the old basis.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook