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Homework Help: 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]
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