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Quick Braket notation question

  1. Jan 3, 2010 #1
    I'm a complete noob with Braket and i've only just started getting to grips with it.

    For completeness' sake though (from the book i'm currently reading), I can't seem to find a definition for:

    [itex]\langle J_z \rangle[/itex]

    Would this just be the "magnitude" of [itex]J_z[/itex]?

  2. jcsd
  3. Jan 3, 2010 #2


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    It's an expectation value, i.e. the average result in a (long) series of measurements of Jz on identically prepared systems.
    Note that it depends on what state the system is in.

    This post should be useful if you're learning bra-ket notation.
  4. Jan 3, 2010 #3


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    Actually it's the expectation value of [itex]J_z[/itex] - that is,
    [tex]\langle J_z \rangle = \langle \psi \vert J_z \vert \psi \rangle[/tex]
    In order to actually evaluate that expression, you would have to have some quantum state [itex]\vert\psi\rangle[/itex], since the expectation value of any operator depends on the quantum state.
  5. Jan 3, 2010 #4
    Ah crud, I completely forgot that's how you write Expectation value.

    so, just to confirm I have a grip on this,

    [itex]\langle x \rangle = \langle \psi \vert {x} \vert \psi \rangle = \int_{-\infty}^{\infty} \psi^* x \psi dx [/itex]

    Is that right? Assuming the limits are from infinity to minus infinity.

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