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Very Basic questions on bra-ket notation

  1. Sep 14, 2011 #1
    Hello,

    i am a beginner in quantum mechanics and i have those basic questions on the bra-ket notation:

    Which dimension has a ket [itex] | \phi >[/itex] describing a state normally? Maybe[itex] \quad C ^n[/itex]?

    Which dimension has a bra-ket [itex] <\psi | \phi >[/itex]then? Maybe [itex] \quad C [/itex]?

    How do you get the matrix representation of an operator in general? I have been reading something like this: [itex] <\phi_n |\hat{A}| \phi_m >[/itex]? I think i have to figure out then, how A works on phi_m but what to do next?

    Thanks for helping
     
  2. jcsd
  3. Sep 14, 2011 #2

    Fredrik

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    See post #3 here for the relationship between matrices and linear operators. This old post explains bra-ket notation.

    What do you mean by "dimension"? Do you mean in the sense of units? I have never seen a reason to assign them a unit, so I would consider them dimensionless. Note that [itex]|\langle\alpha|\beta\rangle|^2[/itex] must be dimensionless since it's supposed to be interpreted as a probability.
     
  4. Sep 14, 2011 #3

    dextercioby

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    A vector or a scalar has no dimension, a space of vectors has. Yes, if phi_n is a set of vectors which form a basis in a (pre-)Hilbert space, then [itex] \langle \phi_n, A \phi_n\rangle [/itex] is a matrix element, a complex number.
     
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