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Dual of an HO energy eigenket

  1. Jul 7, 2014 #1
    Hi.

    This is clearly wrong, but I don't know where is the error:
    ##\langle n\vert = (\vert n \rangle )^* = (a_+^n\vert 0 \rangle )^* = \langle 0\vert a_{-}^n = 0 ##
     
  2. jcsd
  3. Jul 7, 2014 #2
    The error is in the last step. If ##a_{-}## is the lowering operator, ##a_{-}|0\rangle = 0##, but ##\langle 0 | a_{-} = \langle 1 | \neq 0##. To see this, take the conjugate of the equation ##a_{+}|0\rangle = |1\rangle##.
     
  4. Jul 8, 2014 #3
    Oh, ok, that explains it. Thank you.
     
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