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H(t1+t2) = Ht1+Ht2

  1. Jan 3, 2010 #1
    Hello,
    Is it correct to say that H(t1+t2)=Ht1+Ht2? I think it's true but I can't say exacly why.
    And also, is it true that Ht2*Ht1-Ht1*Ht2=0?
    would the answer change if we know the operator is harmitian or not?
    Do you have any idea where can I find a summary about operators ?

    Thanks
     
  2. jcsd
  3. Jan 3, 2010 #2
    Re: Operators

    An operator which commutes under addition and subtraction is called a linear operator, i.e. H is linear iff

    H(t1+t2)=Ht1+Ht2, and
    H(ct)=c(Ht).

    It can be shown that every Hermitian operator is linear and commutes with itself ( [H,H]=0 ).

    If you don't know the operator is Hermitian, or linear, then the commutativity requires proof.

    Search wolfram mathworld for more info, http://mathworld.wolfram.com/LinearOperator.html
     
    Last edited: Jan 3, 2010
  4. Jan 3, 2010 #3

    Fredrik

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    Re: Operators

    Are the t's vectors? Is H(t) supposed to be a time-dependent (Heisenberg picture) operator? If it's the latter, use A(t)=exp(iHt)A exp(-iHt).

    I suggest you check out this book, but almost any book on QM or linear algebra will do.
     
    Last edited: Jan 3, 2010
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