1. Not finding help here? Sign up for a free 30min 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!

Basic Quantum Manipulation

  1. May 26, 2012 #1
    Hey guys, I need some help understanding some very basic quantum manipulation techniques.

    If I am working out the bra version of a tensor product on some ket vectors, do the two ket vectors change from |v1>|v2> to <v1|<v2|, or to <v2|<v1|.

    Or, to put in context, if I measure an operator with an eigenvector AxB on state |v1>|v2> , is the probability that I get the eigenvalue associated with this eigevector

    <v1|<v2|AxB|v1>|v2> or <v2|<v1|AxB|v1>|v2>?​

    Many thanks for looking through this with me
     
  2. jcsd
  3. May 29, 2012 #2
    If [itex]|v_1\rangle|v_2\rangle[/itex] is a state is the tensor product [itex]\mathcal{H}_1 \otimes \mathcal{H}_2[/itex] of two Hilbert spaces, then the corresponding bra is in the tensor product of the dual spaces of the Hilbert spaces, namely [itex]\mathcal{H}_1^* \otimes \mathcal{H}_2^*[/itex]. Thus, it is [itex]\langle v_1|\langle v_2|[/itex].
    Btw, a more precise notation is [itex]|v_1\rangle\otimes|v_2\rangle\equiv|v_1\rangle|v_2\rangle[/itex] and [itex]\langle v_1|\otimes\langle v_2|\equiv\langle v_1|\langle v_2|[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook