Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Direct products

  1. Feb 4, 2015 #1


    User Avatar

    I have just started looking at direct products and came across the following which i don't understand :

    the direct product of two spin -up vectors = | 1 > which is in a bigger vector space

    I don't understand how the direct product is | 1 > ? and in this case is it always a bigger vector space or the same size as the original vector spaces ?
  2. jcsd
  3. Feb 4, 2015 #2


    User Avatar
    Science Advisor

    That's just sloppy notation. If you are trying to understand direct product, it's basically just making an ordered pair of the two vectors.
    |up1> x |up2> = |up1, up2>
    Now clearly, the total z angular momentum of |up1, up2> is 1hbar so we can also label this state |1>. But that's just notation, not math.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook