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

Outer product problem of derac notation

  1. Jan 26, 2009 #1
    why |a><b| expresses the projection...how can it be possible on matrix..if we multiply a ket a with a bra b ...we get a product of two matrix(one is a column matrix,an0ther is row matrix)..from where nothing can be realized very clearly..how this multiplication of matrix can give a projection..??
     
  2. jcsd
  3. Jan 26, 2009 #2

    strangerep

    User Avatar
    Science Advisor

    Think of the ket as a column vector, and the bra as a row vector.
    So braket gives a scalar, but ketbra gives a square matrix.
     
  4. Jan 27, 2009 #3
    I know ket bra is a square matrix...but what is the especiality of this squar matrix??how it expresses projection.
     
  5. Jan 27, 2009 #4

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    (|a><a|)*|b> = <a|b>|a>

    It projects from the state |b> the part of it which is parallel to |a>
     
  6. Jan 27, 2009 #5
    plzz i know those..but i want the matrix format..if |A>=a
    b
    c
    and <B|={d,e,f}. now perform a matrix multiplication this two matrix..and it will give u a result.and how this odd looking matrix express the projection..that was my question.
     
  7. Jan 27, 2009 #6

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    In what basis do you want to represent the operator |a><b| ?

    (|a><a|)*|b> = <a|b>|a>

    IS a matrix multiplying the ket |b> !!!
     
  8. Jan 27, 2009 #7
    Look at it in a basis where |a> is a basis state
    [tex]|a\rangle =\begin{pmatrix} 1\\0\\0\end{pmatrix}[/tex]
    then the matrix |a><a| will be
    [tex] |a\rangle\langle a|=\begin{pmatrix} 1 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0\end{pmatrix}[/tex]
    acting with this on any vector
    [tex]|b\rangle=\begin{pmatrix} c\\ d\\ e\end{pmatrix}
    [/tex]
    will give you just

    [tex](|a\rangle\langle a|)|b\rangle=\begin{pmatrix} c \\ 0 \\ 0 \end{pmatrix}=\langle a| b\rangle |a\rangle[/tex]

    Does this help?
     
  9. Jan 27, 2009 #8

    malawi_glenn

    User Avatar
    Science Advisor
    Homework Helper

    u must choose basis of representation for your kets and bras as shown by jensa.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Outer product problem of derac notation
Loading...