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Help on the expectation value of two added operators

  1. Sep 28, 2013 #1
    Hi everyone,

    I was just working on some problems regarding the mathematical formalism of QM, and while trying to finish a proof, I realized that I am not sure if the following fact is always true:

    Suppose that we have two linear operators A and B acting over some vector space. Consider a state ket | [itex]\psi[/itex] >

    I am wondering if
    < [itex]\psi[/itex] | (A+B) | [itex]\psi[/itex] > = < [itex]\psi[/itex] | A | [itex]\psi[/itex] > + < [itex]\psi[/itex] | B | [itex]\psi[/itex] >
    is always true?

    I am thinking that it IS true.

    My attempt at the problem, is of course to try and show that
    (A+B) | [itex]\psi[/itex] > = A | [itex]\psi[/itex] > + B | [itex]\psi[/itex] >
    But I am having trouble finding a definition which will confirm this to always be true.

    I feel like I am completely overlooking something. Does any one have a helpful hint for me? ANy literature to point me to? My linear algebra books are failing me on this one, at first glance.
     
  2. jcsd
  3. Sep 28, 2013 #2

    Simon Bridge

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    Definition of a linear operator?
     
  4. Sep 28, 2013 #3
    Checkout Principles of Quantum Mechanics (P.A.M. Dirac) chapter II, Dynamical Variables and Observables, section 7, Linear Operators.
     
  5. Sep 28, 2013 #4
    THANK YOU! I don't know why this was so hard to find, but this is exactly the sort of thing I was looking for!
     
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