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Quick bra-ket question

  1. Jan 19, 2012 #1
    |t> + |a> = ?? As an angle from the transition axis

    now I know it is 45 degrees is the answer but I am not sure what |t> or |a> equals.
    I know |theta> = cos theta |t> + sin theta |a>
    so how do I go from here?
    Does |t> = cos^2 theta
    and |a> = sin^2 theta????

    Thanks.
    Stephen
     
  2. jcsd
  3. Jan 20, 2012 #2
    Your notation makes no sense to me, maybe you should write down the problem exactly as it was stated?
     
  4. Jan 20, 2012 #3
    What states of polarization do the following states represent(specify by an angle from the transmission axis of the polarizer).
    a.

    |t> + |a>
     
  5. Jan 20, 2012 #4
    I still think I would need much more information to answer this question. Do you use some convention in your class what |t> and |a> mean?
     
  6. Jan 20, 2012 #5
    That is what I am trying to find out

    |t> is the transmission quantum state
    |a> is the absorbtion quantum state

    The lecture started with
    |p> = cos theta |t> + sin theta |a>
    and
    <t|p> = cos theta
    <a|p> = sin theta
     
  7. Jan 20, 2012 #6
    bump...

    would |t> be cos theta
    and |a> sin theta

    what would these represent where
    |t> + |a> is 45 degrees
    |t> + 2|a> is 63 degrees
    2|t> - |a> is 27 degrees

    please help me figure out what |t> and |a> represent!!!

    Thanks.
     
  8. Jan 23, 2012 #7
    uhh just guessing but by looking at that notation, |p> = |t> should represent a state that will be transmitted 100% of the time, and |p> = |a> represents a state that will be absorbed 100% of the time. So a state |p> =1/sqrt(2)[ |t> + |a> ] should represent a state thats in a superposition of these two states, and so there is a 50/50 chance of it being absorbed or transmitted when it encounters the polarizing filter. So quantum mechanically the state of the system is either |t> or |a> when it interacts with the polarizer and that decides whether or not it is transmitted. I guess this would translate classically to a polarizer whose angle is at 45degrees, since as you said, |p> = cos theta |t> + sin theta |a>. The polarizing angle just determines how much of each of the states |a> and |t> you have at any given time. They are orthogonal states.
     
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