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Wave Equations in Bras and Kets

  1. Oct 11, 2011 #1
    My texts aren't exactly clear on how to handle equations of this sort:

    |ψ>=c(1|1>+2|2>-3|3>)

    How is one to interpret this? All I'm sure of is that |ψ> is ψ(x) and that c is the normalization constant (which would be solved for in the usual way). Any tips or pointers towards resources for further study are greatly appreciated!
     
  2. jcsd
  3. Oct 12, 2011 #2

    vela

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    It's a vector equation, like
    [tex]\vec{x} = c(1\vec{v}_1+2\vec{v}_2-3\vec{v}_3)[/tex]
    [itex]\psi(x)[/itex] is actually the amplitude [itex]\langle x \vert \psi \rangle[/itex]. Consider
    [tex]\vert \psi \rangle = \int dx\,\lvert x \rangle\langle x \rvert \vert \psi \rangle = \int dx\,\vert x \rangle \langle x \vert \psi \rangle = \int dx\, \psi(x) \vert x \rangle[/tex]to see what [itex]\psi(x)[/itex] means in a linear algebra sense.
     
    Last edited: Oct 12, 2011
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