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Ket Vectors

  1. Oct 28, 2015 #1
    In Dirac's "The Principles of Quantum Mechanics," ket vectors are multipled by complex numbers (c1 |A> + c2 |A> = c1 + c2 |A>) and I was curious what affect this has a) on the ket vector and b) on the entire system? Also is (c1 |A> + c2 |A> = c1 + c2 |A>) equal to (|A> + |A> = |A>)? Thank you for your help!
     
  2. jcsd
  3. Oct 28, 2015 #2
    At this level, just think about ket vectors as ordinary column vectors from any introductory text on linear algebra.

    a) If you multiply a vector by a complex scalar, it means you multiply each component in the vector by the scalar.

    b) No, |A> + |A> = 2|A>.
     
  4. Oct 28, 2015 #3

    Doc Al

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    Staff: Mentor

    As far as the ket itself goes, multiplying it by some complex number has no physical significance. c1 |A> and (c1 + c2) |A> would refer to the same state. (For mathematical convenience, we usually normalize the state.)

    When you are composing a state out of several different kets, then those coefficients are significant as they reflect the relative phase of each ket in the overall state.

    I think you missed a factor of 2 there.
     
  5. Oct 28, 2015 #4
    Thank you very much for your time; it's very helpful.
     
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